Related papers: On the combinatorics of Forrester-Baxter models

Let $X$ be a finitely generated left module over a left artinian ring $R$, and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where $l_i$ is the length of the $i$-th term of the minimal projective resolution of $X$. We…

We study polynomial identities satisfied by the mutation product $xpy - yqx$ on the underlying vector space of an associative algebra $A$, where $p, q$ are fixed elements of $A$. We simplify known results for identities in degree $4$,…

This paper presents a symbolic computation method for automatically transforming $q$-hypergeometric identities to $q$-binomial identities. Through this method, many previously proven $q$-binomial identities, including $q$-Saalsch\"utz's…

In this paper, we first determine the minimum possible size of an Fq-linear set of rank k in PG(1, q^n). We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a…

Muscalu, Tao, and Thiele prove $L^p$ estimates for the "Biest" operator defined on Schwartz functions by the map \begin{align*} \hspace{5mm} C^{1,1,1}:& (f_1, f_2, f_3) \mapsto \int_{\xi_1 < \xi_2< \xi_3} \left[ \prod_{j=1}^3 \hat{f}_j…

We evaluate $q$-Bessel functions at an infinite sequence of points and introduce a generalization of the Ramanujan function and give an extension of the $m$-version of the Rogers-Ramanujan identities. We also prove several generating…

We provide a combinatorial description of morphisms in the coherent sheaf category ${\rm coh}\mbox{-}\mathbb{X}(p,q)$ over weighted projective line of type $(p,q)$ via a marked annulus. This leads to a geometric realization of exceptional…

We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…

We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime $p$. In particular, we obtain nontrivial results about the number of solution in boxes with the side…

We provide a refined combinatorial identity for the set of partitions of $\{1,\dots, n\}$, which plays an important role in investigating several limit theorems related to finite free convolutions. Firstly, we present the finite free…

The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set,…

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten…

We state and prove the $q$-extension of a result due to Johnston and Jordaan (cf. \cite{Johnston-2015}) and make use of this result, the orthogonality of $q$-Laguerre, little $q$-Jacobi, $q$-Meixner and Al-Salam-Carlitz I polynomials as…

Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimension r and singular locus of dimension at most s, and let…

We obtain q-analogues of the Sylvester, Ces\`aro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.

Let $\mathbb C$ be the set of complex numbers, and let $\mathcal P$ be a collection of complex polynomial maps in several variables. Assuming at least one $P\in\mathcal P$ depends on at least two variables, we classify all possibilities for…

We begin a generalized study of sum-product type phenomenon in different fields by considering pairs $P(x,y)$ and $Q(x,y)$ of two variable polynomials that simultaneously exhibit small symmetric expansion. Our first result is that such…

We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for $U_q\widehat{sl(n)}$ restricted interaction round a face (IRF) models. The evaluation of momenta by adding…