Related papers: Enumerative Properties of NC^B(p,q)
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower…
We consider some $q$-series which depend on a pair of positive integers $(k,m)$. While positivity of these series holds for the first few values of $(k,m)$, the situation is quite unclear for other values of $(k,m)$. In addition, our series…
Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of $\epsilon$-noncrossing partitions. It is shown that the set of such partitions forms a lattice, which interpolates as a poset…
The functional equation f(p(z))=g(q(z)) is studied, where p,q are polynomials and f,g are trancendental meromorphic functions in C. We find all the pairs p,q for which there exist nonconstant f,g satisfying our equation and there exist no…
We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for self-dual cyclic square-lattice strips of various widths $L_y$ and arbitrarily great lengths $L_x$, with $Q$ and $v$ restricted to satisfy the relation…
In this paper, we study a family of single variable integral representations for some products of $\zeta(2n+1)$, where $\zeta(z)$ is Riemann zeta function and $n$ is positive integer. Such representation involves the integral…
We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is…
We seek simple conditions on a pair of labeled posets that determine when the difference of their $(P,\omega)$-partition enumerators is $F$-positive, i.e., positive in Gessel's fundamental basis. This is a quasisymmetric analogue of the…
We continue the study of the $(a,b,m)$-copartition function $\mathrm{cp}_{a,b,m}(n)$, which arose as a combinatorial generalization of Andrews' partitions with even parts below odd parts. The generating function of $\mathrm{cp}_{a,b,m}(n)$…
Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read-Rezayi state, the Bonderson-Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the…
In this work, we consider the generating function of Kim's q-Euler polynomials and introduce new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give surprising identities for studying in Analytic Numbers…
An extension to triangular domains of the univariate q-Bernstein basis functions is introduced and analyzed. Some recurrence relations and properties such as partition of unity and degree elevation are proved for them. It is also proved…
In this paper we will give a M\"obius number of $NC^{k}(W) \setminus \bf{mins} \cup \{\hat{0} \}$ for a Coxeter group $W$ which contains an affirmative answer for the conjecture 3.7.9 in Armstrong's paper [ Generalized noncrossing…
We consider the processes $g\to W{+}\,q'$ and $q\to Z{+}\,q$ and derive the respective splitting functions as functions of two kinematic variables: the longitudinal momentum fraction $z$ and transverse momentum $p_T$ of the produced bosons…
The study of arithmetic properties of coefficients of modular forms $f(\tau) = \sum a(n)q^n$ has a rich history, including deep results regarding congruences in arithmetic progressions. Recently, work of C.-S. Radu, S. Ahlgren, B. Kim, N.…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
For each pair of coprime integers $a$ and $b$ we have a rational $q$-Catalan number $\operatorname{Cat}(a,b)_q=\binom{a+b}{a}_q/[a+b]_q$. It is known that this is a polynomial in $q$ with nonnegative integer coefficients, but the nature of…
We study the properties of a function $\psi(z, q)$ (the generalized polygamma function), intimately connected with the Hurwitz zeta function and defined for complex values of the variables $z$ and $q$, which is entire in the variable $z$…
Given a non-negative integer $q$, we study two different notions of the $q$-capability of Lie algebras via the non-abelian $q$-exterior product of Lie algebras. The first is related to the $q$-crossed modules and inner $q$-derivations, and…
Let $\mathbb{F}_q$ denote the finite field of $q$ elements with characteristic $p$. Let $\mathbb{Z}_q$ denote the unramified extension of the $p$-adic integers $\mathbb{Z}_p$ with residue field $\mathbb{F}_q$. In this paper, we investigate…