Related papers: Enumerative Properties of NC^B(p,q)

A combinatorial study of multiple $q$-integrals is developed. This includes a $q$-volume of a convex polytope, which depends upon the order of $q$-integration. A multiple $q$-integral over an order polytope of a poset is interpreted as a…

The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients. This readily follows from the $q$-binomial theorem, or the…

Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic…

We obtain new non-existence results of generalized bent functions from \ZZ^n_q to \ZZ_q (called type [n,q]). The first case is a class of types where q=2p_1^{r_1}p_2^{r_2}. The second case contains two types [1 <= n <= 3, 2 * 31^e]$ and [1…

It was recently shown that $q\omega(q)$, where $\omega(q)$ is one of the third order mock theta functions, is the generating function of $p_{\omega}(n)$, the number of partitions of a positive integer $n$ such that all odd parts are less…

We introduce two polynomials (in $q$) associated with a finite poset $P$ that encode some information on the covering relation in $P$. If $P$ is a distributive lattice, and hence $P$ is isomorphic to the poset of dual order ideals in a…

We study certain algebras of theta-like functions on partitions, for which the corresponding generating functions give rise to theta functions, quasi-Jacobi forms, Appell-Lerch sums, and false theta functions.

By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions…

By work of Bringmann, Ono, and Rhoades it is known that the generating function of the $M_2$-rank of partitions without repeated odd parts is the so-called holomorphic part of a certain harmonic Maass form. Here we improve the standing of…

Let q be an odd positive integer and P \in F2[z] be of order q and such that P(0) = 1. We denote by A = A(P) the unique set of positive integers satisfying \sum_{n=0}^\infty p(A, n) z^n \equiv P(z) (mod 2), where p(A,n) is the number of…

Negabent functions were introduced as a generalization of bent functions, which have applications in coding theory and cryptography. In this paper, we have extended the notion of negabent functions to the functions defined from…

Let $p$ and $q$ be polynomials with degree $2$ over an arbitrary field $\mathbb{F}$. In the first part of this article, we characterize the matrices that can be decomposed as $A+B$ for some pair $(A,B)$ of square matrices such that $p(A)=0$…

We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact…

We introduce a new class of reflection groups associated with the canonical bilinear lattices of Lenzing, which we call reflection groups of canonical type. The main result of this work is a categorification of the corresponding poset of…

We obtain new nonexistence results of generalized bent functions from $\{Z^n}_q$ to $\Z_q$ (called type $[n,q]$) in the case that there exist cyclotomic integers in $ \Z[\zeta_{q}]$ with absolute value $q^{\frac{n}{2}}$. This result…

The aim of this paper is to define and study pointed and multi-pointed partition posets of type A and B (in the classification of Coxeter groups). We compute their characteristic polynomials, incidence Hopf algebras and homology groups. As…

In this Ph.D dissertation (University of Virginia, 2022), we prove results about the coefficients of partition-theoretic generating functions and of coefficients of integer weight modular forms. Using various forms of the circle method, we…

For each prime p other than 3, and each power q=p^k, we present two large classes of permutation polynomials over F_{q^2} of the form X^r B(X^{q-1}) which have at most five terms, where B(X) is a polynomial with coefficients in {1,-1}. The…

We conjecture that, if the quotient of two $q$-binomial coefficients with the same top argument is a polynomial, then it has non-negative coefficients. We summarise what is known about the conjecture and prove it in two non-trivial cases.…

The generating function for the number of purely crossing partitions of {1,...,n} is found in terms of the generating function for Bell numbers. Further results about generating functions for asymptotic moments of certain random Vandermonde…