Papers

The Burrows–Wheeler transform is usually viewed as a clustering transform: it tends to group equal letters into long runs. We study the opposite extremal regime, where the BWT output is completely unclustered, that is, has as many equal-letter runs as positions. Known results imply, on the one hand, that the number of runs in the BWT of a Lyndon word can increase by at most a factor of two, and, on the other hand, that over every alphabet of size at least three completely unclustered BWT images exist in every length. This leads to the extremal problem lying between these two facts. For \(k\ge3\), let \(U_k(n)\) be the minimum cyclic run number of a primitive necklace of length \(n\) whose BWT has \(n\) runs. We prove the universal lower bound \(U_k(n)\ge\lceil n/2\rceil\), reduce the sharpness problem for one-cycle BWT images \(L\) to the Hamming identity \[ \cruns(\BWT^{-1}(L))=\dH(L,\sort(L)), \] and develop a natural multiset-of-necklaces relaxation with an explicit constant-cycle correction. We compute the small values, including the exceptional value \(U_k(6)=4\), prove a parity obstruction for the Parikh vectors of sharp examples, and determine the multiset relaxation exactly. Finally, for every prime \(p\equiv5\pmod8\) for which \(2\) is a primitive root modulo \(p\), we prove sharpness in the adjacent lengths \(p-1\) and \(p\). Under the corresponding Artin-type infinitude hypothesis, this gives infinitely many adjacent sharp pairs.

Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-burst deletion-correcting codes. Specifically, we first characterize several structural properties of the associated deletion balls. Then, leveraging these properties, we derive several upper bounds and a combinatorial lower bound on the maximum size of such codes. As a consequence, our bounds improve upon the previously known results for general parameter regimes and are shown to be asymptotically optimal for certain cases.

In this paper, we extend Mazzola's model of two-voice counterpoint to three-voice first-species counterpoint. The construction combines a fiber product over a shared lower voice with a harmonic mask and a two-stage maximization defining admitted successors. For the Fuxian dichotomy, we compute the successor relation and investigate connections with the Riemann dichotomy and neo-Riemannian transformations. Among pairs of same-mode triads, the model admits the most transporter realizations exactly at the pairs that generate Mazzola's Riemann monoid, but it does not single out the dominant-tonic pair, and it admits only 12 of the 192 parsimonious neo-Riemannian realizations, largely because it excludes transitions that keep a pair of voices stationary.

An edge-colored graph is called rainbow if all its edges have distinct colors. For a fixed graph $H$, the rainbow Turán number $\exstar(n, H)$ is the maximum number of edges in a properly edge-colored graph with $n$ vertices that does not contain a rainbow subgraph isomorphic to $H$. A $t$-fan $\Ft$ ($t \geq 2$) is a graph formed by $t$ triangles sharing a common vertex. A wheel graph $\Wn$ is constructed by connecting a new vertex $x$ to all vertices of a cycle $\Cn$ with $n$ vertices. Keevash, Mubayi, Sudakov, Verstraëte~({\small Combin. Probab. Comput., 2007}) showed that \[ \exstar(n, F_t) \geq \floor{\frac{n^2}{4}} + (t-1)\floor{\frac{n}{2}} \] by constructing extremal graphs for $n\not\equiv 2\pmod 4$. In this paper, we propose such a method: for a graph $H$, the upper bound of $\exstar(n, H)$ can be analyzed using the rainbow Turán number of $H'$, where $H'$ is obtained by deleting one vertex from $H$. By applying this method, we determine the exact values of the rainbow Turán numbers for two families of graphs when the number of vertices $n$ is sufficiently large. Specifically, we obtain: (1) when $n > 230t$, \[ \exstar(n, \Ft) = \floor{\frac{n^2}{4}} + (t-1)\floor{\frac{n}{2}} - \Dn, \] where $\Dn = 1$ if $n \equiv 2 \pmod{4}$, and $\Dn = 0$ otherwise; (2) for graphs $H$ satisfying $W_{2t} \subset H \subset \Kts$ ($t \leq s$), when $n$ is sufficiently large, \[ \exstar(n, H) = \begin{cases} \floor{\frac{n^2}{4}} + \floor{\frac{(t-1)n}{2}} - \Dn & \text{if } t \text{ is odd}, \\ \floor{\frac{n^2}{4}} + \floor{\frac{(t-1)n}{2}} & \text{if } t \text{ is even}. \end{cases} \]

We show that the conflated expression graph for an arbitrary permutation has a unique minimal element and a unique maximal element, and every reduced expression sits on a maximal chain from the source to the sink. This generalizes the work of Manin-Schechtman regarding higher Bruhat orders, and gives an independent and self-contained proof of certain results in Hothem. In addition, we give explicit algorithms for elements in the top and bottom commutation classes. Given any reduced expression $\rho$, we give an explicit method for producing a maximal chain containing $\rho$.

Let $G$ be a simple graph with degree diagonal matrix $D(G)$ and adjacency matrix $A(G)$. The signless Laplacian matrix of $G$ is defined as $Q(G)=D(G)+A(G)$. For a real number $\alpha \in [0, 1]$, Nikiforov (2017) proposed the $A_\alpha$-matrix of a graph $G$ as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$. The $A_\alpha$-spectral radius of $G$, denoted by $\rho_\alpha(G)$, is the largest eigenvalue of $A_\alpha(G)$, where $\rho_0(G)=\rho(G)$ is the spectral radius of $A(G)$ and $2\rho_{\frac{1}{2}}(G)=q(G)$ is the spectral radius of $Q(G)$. Sun and Das (2020) proved that for any non-isolated vertex $v$ of degree $d_v$, $\rho^2(G)-\rho^2(G-v) \leq 2 d_v-1$, which confirmed the conjecture originally posed by Guo, Wang, and Li (2019). Recently, Liu and Ning (2026) provided a short and self-contained proof of this inequality. In this paper, we establish the corresponding result for $\rho_\alpha(G)$. As a corollary, for every $k\in [0,d_v+1]$, we have $$ \rho^2(G)- \rho^2(G-v) \leq 2d_v-1 +(k-2)\left(\frac{d_v}{\rho(G)}-1\right). $$ This inequality coincides with that of Sun and Das when $k=2$, and is strictly sharper than theirs whenever $k\neq 2$ and $d_v\neq \rho(G)$. We also give a short proof of the inequality $\rho_{\alpha}(G)-\rho_{\alpha}(G-v)\leq \alpha +\frac{(1-\alpha)^2d_v}{\rho_{\alpha}(G)-\alpha d_v}$, which is obtained by Wang and She (2022). Moreover, we obtain a unified generalization of Hong, Shu and Fang's inequality for $\rho(G)$ and Nikiforov's inequality for $q(G)$ in terms of $\rho_\alpha(G)$.

Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over matrix rings with coefficients in finite fields. We show that these graphs exhibit several interesting graph-theoretic properties. Along the way, we also prove some results on the structure of matrix rings, which may be of independent interest.

Given a graph $G$, a set $F$ of edges is an edge dominating set of $G$ if every edge in $G$ is either in $F$ or adjacent to an edge in $F$. A graph $G$ is said to be well-edge-dominated if every minimal edge dominating set has the same cardinality. This definition is the edge version of domination in that a set $D\subseteq V(G)$ is a dominating set if every vertex in $G$ is in $D$ or adjacent to a vertex in $D$ and the domination number $\gamma(G)$ is the minimum cardinality among all dominating sets. In this paper, we complete the characterization of all nonbipartite, well-edge-dominated graphs. In addition, we produce an infinite class of graphs that satisfy the well-known Vizing's conjecture in domination theory that states $\gamma(G\Box H) \ge \gamma(G)\gamma(H)$ where $G\Box H$ is the Cartesian product of $G$ and $H$.

Using the concepts of Eulerian-spanning set and coboundary operator, we generalize Hadlock's conversion of the maxcut problem on planar graphs to one on general graphs with non-negative weights. Using our conversion, we can explore algorithms for maxcut beyond the class of planar graphs. We obtain a Fixed-Parameter Tractable algorithm for $k$-contraction apex graphs. Specifically, our algorithm can be applied to graphs with crossing number $k$, giving an $O(2^k(n+k)^{3/2}\log (n+k))$-time algorithm that matches the best known results when restricted to non-negative weights.

Let $\kappa^{\prime}(G)$ be the edge-connectivity of the graph $G$. The strength of $G$, denoted by $\overline{\kappa}^{\prime}(G)$, is the maximum edge-connectivity of its subgraphs. A simple graph $G$ is called $k$-edge-maximal if $\overline{\kappa}^{\prime}(G) \leq k$ but for any edge $e$ not in $G$, $\overline{\kappa}^{\prime}(G+e) \geq k+1$. In this paper, we propose the concepts of kernel and closure of a graph and discuss the properties of closure. Utilizing these properties, we present the necessary and sufficient condition for a graph to be $k$-edge-maximal, which refines the results in [J. Graph Theory 14 (1990) 187–197], and prove that there exists a $k$-edge-maximal graph of order $n$ with $m$ edges if and only if $m=(n-1)k-\binom{k}{2}r$, for some integer $r$ with $1\leq r\leq \left\lfloor \frac{n}{k+2}\right\rfloor$. Furthermore, we characterize the structure of $k$-edge-maximal graphs with a given number of edges.

We solve, for all sufficiently large even orders, the problem proposed by Chen et al. on sharp $A_\alpha$-spectral conditions for the existence of odd $[1,b]$-factors when $\alpha>1/2$. Chen et al. showed that every connected graph of even order $n$ with no odd $[1,b]$-factor has $A_\alpha$-spectral radius at most $\max_{1\le s\le k}\rho_\alpha(G_s)$, where $G_s=K_s\nabla\left(K_{n-(b+1)s-1}\cup(bs+1)K_1\right)$ and $k=\lfloor(n-2)/(b+1)\rfloor$. Thus the problem reduces to finding the graph with the largest $A_\alpha$-spectral radius among these obstruction graphs. We prove that, for every $\alpha\in(1/2,1)$, $\max_{1\le s\le k}\rho_\alpha(G_s)=\max\{\rho_\alpha(G_1),\rho_\alpha(G_k)\}$. Moreover, for each fixed odd $b\ge 3$ and every even $n\ge N_b=(b+1)\max\{2b+3,14\}+2$, there exists a unique $\alpha=\alpha_\ast(n,b)\in(1/2,1)$ at which $\rho_\alpha(G_1)=\rho_\alpha(G_k)$. Consequently, $G_1$ is the unique extremal graph for $1/2<\alpha<\alpha_\ast(n,b)$, both $G_1$ and $G_k$ are extremal at $\alpha=\alpha_\ast(n,b)$, and $G_k$ is the unique extremal graph for $\alpha_\ast(n,b)<\alpha<1$. This gives the exact $A_\alpha$-spectral threshold, together with the sharp exceptional graphs, for odd $[1,b]$-factors when $\alpha>1/2$ and $n\ge N_b$.

We give a spectral realization of the Robinson-Schensted-Knuth (RSK) correspondence in terms of the representation theory of the symmetric group $S_n$ and the degenerate affine Hecke algebra (AHA) $H_n$. We view RSK, which builds a pair of standard Young tableaux from a permutation, as a special case of rectification, also known as Jeu de Taquin, which turns skew tableaux into straight ones. In this framing, the initial permutation corresponds to a skew tableau of staircase shape. To interpret this in terms of representation theory, take permutations to label weight vectors in a generic $H_n$-module $V(a_1, \ldots , a_n)$, which is isomorphic to $\mathbb{C}[S_n]$ as an $S_n$-module. Writing permutations as staircases amounts to placing these weight vectors inside the regular representation of a larger symmetric group containing $S_n$; more geometrically, we push $S_n$ to the right toward infinity so its Jucys-Murphy (JM) elements have enough room to represent the external translations of $H_n$. Then, rectification corresponds to squeezing out this extra room from the left, leaving only $S_n$ and its regular JM elements as the limit of the external translations. By expressing slides via sequences of exchanges of consecutive values inside the tableau, we can model rectification by an operator acting on the regular representation. This lets us explicitly write down the change of basis between $H_n$-weight vectors and $S_n$-weight vectors, where the latter are eigenvectors of the JM elements in $S_n$ acting both on the left and on the right, and hence labeled by pairs of standard tableaux. The resulting correspondence between the labels of the weight vectors is exactly RSK.

Let $G$ be a simple connected graph, and let $T_{G}(x,y)$ be the Tutte polynomial of $G$. Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning forests of $G$ and odd $G$-partitionable permutations, and show that $T_{G}(2,-1)$ is equal to both the number of even-left spanning forests of $G$ and the number of odd $G$-partitionable permutations. In particular, for a complete graph $K_n$, we prove that $T_{K_{n}}(2,-1)$ is the number of alternating permutations on $\{1,2,\dots,n+1\}$, using two distinct techniques: a recurrence relation and an explicit bijection construction.

Motivated by a recent conjecture of Bsila, Cox, Hugo, Styron and Zhuang concerning fixed points and pixed points on pattern-avoiding permutations, we prove a bivariate refinement involving descent statistics. Given a set of permutations $\Pi$, let $\mathfrak{S}_n(\Pi)$ denote the set of permutations in the symmetric group $\mathfrak{S}_n$ that avoid every element of $\Pi$ in the sense of pattern avoidance. For each set $\Pi$ appearing in their conjecture, we show that the pairs of statistics $(\mathrm{des},\mathrm{fix})$ and $(\mathrm{ides},\mathrm{pix})$ are equidistributed over $\mathfrak{S}_n(\Pi)$. Our proof is based on explicit ordinary generating functions for the corresponding pattern-avoiding classes.

We establish a convolution formula for the characteristic polynomial of a finite geometric semilattice $M$: \[ \chi(M,st)=\sum_{X\in \underline{M}} s^{r-{\rm rk}_{\underline{M}}(X)}\chi(\underline{M}^X,t)\,\chi(M_{(X)},s), \] where $\underline{M}$ denotes the centralization of $M$, and $M_{(X)}$ denotes the localization at $X$. This generalizes a nice formula of Southerland, Southern, and Zhou, which is recovered at $s=1$. When specialized to hyperplane arrangements, the identity yields a new expansion closely related to Wang's convolution formula. We further provide a combinatorial interpretation of the convolution formula using the finite field method over $\mathbb{F}_{p^2}$ and $\mathbb{F}_p$.

A cut-edge of a connected graph is an edge whose deletion increases the number of components. In this paper, we first state some conditions for a planar graph to have a few cut-edges. After that, we use the main results to study the conditions for a colored planar graph to have a bounded conflict-free connection number.

In this work, we study the symmetric hit problem in four variables by analyzing the relative cohit space, defined as the kernel of the inclusion-induced map from symmetric to ordinary cohits. Theoretically, we establish that this relative space is isomorphic to a kernel in the first group cohomology of the permutation group and, equivalently, to an $\operatorname{Ext}^1$ kernel for the general linear group, equipped with a canonical action of the normalizer quotient. Furthermore, bypassing conditional descent hypotheses, we utilize explicit Lucas–Cartan identities to construct unconditional fixed Steenrod preimages for nontrivial stabilizers, resolving infinite families of monomials strictly above the minimal-spike weight. Using the ordinary and symmetric Kameko isomorphisms, we reduce the determination of complete bases in two generic degree families to exact calculations in degrees one, three, six, ten, and sixteen. We discover that universal relative vanishing fails: the relative space is non-trivially one-dimensional in degree fifteen and forms an indecomposable two-dimensional normalizer module in degree eighteen. In the family $5\cdot2^t-4$, the symmetric cohit dimension stabilizes at six and the relative dimension at one for $t\geq2$; in the family $7\cdot2^t-4$, they are four and zero for $t\geq1$. We give complete bases by explicit exponent formulas and prove Janfada's monomial implication in every degree of both families. A general numerical threshold determines the finite initial degree from which Kameko isomorphisms apply, and a direct-sum formula transports the entire symmetric hit basis.

We construct explicit isomorphisms between three models for the $B(\infty)$ crystal in type ${\tt A}_1^{(1)}$: affine Mirković–Vilonen polytopes, Kleshchev multipartitions, and a new model we call upper ledge diagrams. We also present some clarifying results on these crystals, giving a direct method for completing an affine MV polytope from the data of one of its boundary root partitions, and a non-iterative recognition theorem which characterizes Kleshchev multipartitions in type ${\tt A}_1^{(1)}$. We apply these results to the representation theory of KLR algebras, where they yield a combinatorial dictionary between cuspidal- and cellular-theoretic frameworks, along with some augmented branching rules for real root functors of induction and restriction.

Ballantine, Beck, and Merca defined the elementary symmetric partition map pre$_j$ that sends a partition $\lambda$ to a larger partition whose parts are the summands appearing in the evaluation of the $j$-th elementary symmetric polynomial on $\lambda$. They conjectured that pre$_j$ is injective on the set of partitions of $n$ with length $\ell \geq j$. The $\ell = j$ case was disproved by Devnani and Eyyunni; they instead conjectured the statement to be true for $\ell > j$. In this article, we answer this refined conjecture in the negative by proving that pre$_j$ is not injective on partitions of $n$ with length $2j$ for $j \geq 3$. We also prove that the analogous map prh$_j$ defined via the complete homogenous symmetric polynomial is injective on the set of all partitions.

We prove that the set of positive integers having between $1$ and $n$ prime factors, counted with multiplicity, has degree of accessibility $2^n$. In particular, the case $n=1$ answers a question of Landman and Robertson asking whether the set of prime numbers is $2$-accessible.

Complementing a theorem of Škrekovski, we characterize the $(h-1)$-critical graphs embeddable in surfaces of Euler genus at least $5$, where $h$ denotes the Heawood number of the surface. Outside of a few small cases, the bulk of our proof is determining the genus of the join of a complete graph and the 5-cycle. As a byproduct of our proof, we also provide a simpler solution to the minimum triangulations problem for nonorientable surfaces using the theory of current graphs.

In 2010, Steurer conjectured that any family of $n$ unit-norm vectors $v_1,\dots,v_n$ with polynomially small average correlation $\mathbb{E}_{i,j}|\langle v_i,v_j\rangle|\leq n^{-\epsilon}$ contains linear-sized constant-separated sets. We refute this conjecture in a strong sense using the machinery of sparse high-dimensional expanders: such vector families do not even have linear-sized $\frac{1}{\log^{1/4-o(1)}(n)}$-separated sets. Consequently, we show that there are families of vertex expanders on $n$ vertices for which the (average) $L_2$-mixing time to the uniform distribution of any reweighted simple random walk is at least $\log^{5/4-o(1)} n$.

The inducibility constant $\lambda_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the case when $F$ has 6 vertices (and there are 78 cases to consider up to isomorphism and complementation). We show that flag algebras can compute the sharp upper bound on $\lambda_F$ in 36 cases of which, as far as the authors know, 30 are new results. In each of the solved cases, we also prove results about the structure of large (almost) extremal graphs. In particular, we establish perfect stability in all 32 cases when the extremal construction has no quasirandom parts. We also present conjectures about the value of $\lambda_{F}$ for 12 further cases (where the upper and lower bounds are very close to each other).

The goal of this work is to study the combinatorics of the lattices of higher torsion classes of the higher Auslander and Nakayama algebras of type A. Combinatorial descriptions of these higher torsion classes were recently obtained by August et al. (2025), and it was observed that the lattices that they form are not semidistributive. We study in some depth these lattices, proving in particular that the lattices of higher torsion classes of the higher Auslander algebras of type A are join-semidistributive, join-extremal and left modular. We also prove that the lattices of higher torsion classes of the higher Nakayama algebras of type A are lattice quotients of them. In order to prove these results, we define a general construction that produces a lattice, which we call $(P,\phi)$-Tamari, for any choice of poset $P$ and chain $\phi$ in $P$. We prove the lattice results for this general construction. When $P=\phi$ is a chain, we recover the Tamari lattice, whereas the lattices of higher torsion classes that we study are obtained for another very particular choice.

The Fourier Entropy-Influence (FEI) conjecture states that the Fourier entropy of Boolean functions is uniformly bounded by their total influence. It has been verified for canonical examples such as disjoint tribes and for some classes of Boolean functions such as symmetric functions and read-$k$ decision trees (with a constant that depends linearly on $k$). In this note we present new classes of Boolean functions that verify the FEI conjecture. The key element is an inequality controlling the difference between the entropy of a function $f$ and the average of the entropies of $f^{\pm}$, the sub-functions obtained by setting $x_m=\pm1$ for some $m$, by the $m$-influence of $f$. If this key inequality were to hold for Boolean functions, then the full FEI conjecture would follow by induction. We introduce the notion of a stopping binary tree and observe that functions that satisfy the key inequality at the branching nodes of the tree and the FEI conjecture at the stopping nodes will satisfy the FEI conjecture. We identify some classes of functions that fit this framework: the $\delta$-tribes functions, the monotone Boolean functions with the tribe separation property, and the Boolean functions with the semi-separation property, and, and, along the way, demonstrate some results that we hope the experts in this fascinating field might find useful.

We develop a new algorithm for computing the second discrete homology group of a graph which is much faster when compared to existing algorithms. To do so, we identify five basic shapes, which are quotient graphs of the 3-cube with the property that the injective maps from them detect all possible 2-boundaries in the singular chain complex computing discrete homology.

We introduce weak and strong poset Ramsey-Turán numbers for $t$-chains in host poset families, focusing on the Boolean lattice family $\mathcal{B}=\{B_n:n\ge 1\}$. For any poset $P$, we show $\operatorname{RT}(\mathcal{B};n,P,l,t)\le \operatorname{RT}^{\sharp}(\mathcal{B};n,P,l,t)$, with equality when $P$ is a chain. In particular, for $t=1$, $\operatorname{RT}(\mathcal{B};n,C_k,l)=\operatorname{RT}^{\sharp}(\mathcal{B};n,C_k,l)=(k-1)(l-1)$. We also give universal upper bounds for both versions. For fixed $k,l,t$ with $\min\{l-1,k-1\}\ge 1$, we prove $\operatorname{RT}^{\sharp}(\mathcal{B};n,A_k,l,t)=\Theta(n^t)$. More generally, for every non-chain poset $P$, the strong number is $\Theta(n^t)$ for fixed $l,t$. Finally, if $h(P)=r>t$ and $l(n)=\lfloor M_n^\beta\rfloor$ with $0<\beta\le \alpha<1$, then both weak and strong versions admit lower bounds of order $\Omega\!\left(2^{\beta n}n^{-\beta/2}\right)$.

We study the space of conformally covariant $n$-point functions of spinning operators using methods from invariant theory, commutative algebra, and combinatorics. We show that the rational part of any such function can be expressed in terms of the basic building blocks introduced by Costa, Penedones, Poland, Rychkov, thereby providing a rigorous proof of a result that is widely used in the physics literature. We reformulate the problem of enumeration of $n$-point structures in terms of counting lattice points in fractional matching polytopes, and compute these counts using vector partition functions, Hilbert functions, and Kostka numbers. We show that all algebraic relations between the building blocks follow from Gram constraints and compute the number of algebraically independent building blocks. For three-point functions, we derive closed counting formulas for arbitrary integer spins, both with and without Bose symmetry, and discuss a necessary and sufficient condition for the partial conservation operator to lift to a differential operator written in terms of the building blocks. We provide code that generates a basis of three-point structures satisfying these constraints for given values of spins and scaling dimensions.

A randomly perturbed digraph is an $n$-vertex directed graph with all out- and in-degrees linear in $n$, to which a linear number (depending on the degree) of random edges have been randomly added. We show that randomly perturbed digraphs whose edges have been colored uniformly with $n$ colors have a rainbow copy of every orientation of every possible length cycle, simultaneously, with high probability. This is a common generalization of work of Araujo, Balogh, Krueger, Piga, and Treglown in the uncolored setting and Katsamaktsis, Letzter, and Sgueglia for consistently oriented spanning cycles. Our proof uses Montgomery's distributive absorption method.

Morier-Genoud and Ovsienko introduced q-deformations of continued fractions, Farey labelings, and Conway–Coxeter friezes, and established relationships among them in restricted settings associated with triangulations having exactly two exterior cells. In this paper, we extend these correspondences to arbitrary subsequences of quiddities arising from general triangulations. We show that the numerator and denominator polynomials of q-deformed continued fractions coincide with entries of q-deformed Conway–Coxeter friezes, while the corresponding polynomials in q-Farey labelings agree with them up to explicit powers of q. These powers are described combinatorially in terms of the number of diagonals in the triangulation, or equivalently, the number of entries equal to 1 in the associated frieze. Furthermore, we determine the minimum and maximum degrees of these polynomials in terms of the same combinatorial data.