相关论文: Rook theory, normal ordering in the $q$-deformed O…

The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…

Given M copies of a q-deformed Weyl or Clifford algebra in the defining representation of a quantum group $G_q$, we determine a prescription to embed them into a unique, inclusive $G_q$-covariant algebra. The different copies are "coupled"…

The aim of the papers is to describe the left regular left quotient ring ${}'Q(R)$ and the right regular right quotient ring $Q'(R)$ for the following algebras $R$: $\mS_n=\mS_1^{\t n}$ is the algebra of one-sided inverses, where…

We first observe a mysterious similarity between the braid arrangement and the arrangement of all hyperplanes in a vector space over the finite field $\mathbb{F}_q$. These two arrangements are defined by the determinants of the Vandermonde…

The Stirling number of a simple graph is the number of partitions of its vertex set into a specific number of non-empty independent sets. In 2015, Engbers et al. showed that the coefficients in the normal ordering of a word $w$ in the…

We solve the normal ordering problem for (A* A)^n where A* (resp. A) are one mode deformed bosonic creation (resp. annihilation) operators satisfying [A,A*]=[N+1]-[N]. The solution generalizes results known for canonical and q-bosons. It…

Dowling showed that the Whitney numbers of the first kind and of the second kind satisfy Stirling number-like relations. Recently, Kim-Kim introduced the degenerate r-Whitney numbers of the first kind and of the second kind, as degenerate…

Let $R$ be a not necessarily commutative ring with $1.$ In the present paper we first introduce a notion of quasi-orderings, which axiomatically subsumes all the orderings and valuations on $R$. We proceed by uniformly defining a coarsening…

We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural…

The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…

The aim of this paper is to give some constructions results of averaging operators on Hom-Lie algebras. The homogeneous averaging operators on $q$-deformed Witt and $q$-deformed $W(2,2)$ Hom-algebras are classified. As applications, the…

In this paper, we define and discuss $\mathcal{R}(p,q)$- deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, P\'olya and inverse P\'olya distributions. We discuss relevant…

Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare characteristic under deformation, it is applied here to compute…

We use rook placements to prove Spivey's Bell number formula and other identities related to it, in particular, some convolution identities involving Stirling numbers and relations involving Bell numbers. To cover as many special cases as…

A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by…

We introduce rook-Eulerian polynomials, a generalization of the classical Eulerian polynomials arising from complete rook placements on Ferrers boards, and prove that they are real-rooted. We show that a natural context in which to…

Remixed Eulerian numbers are a polynomial $q$-deformation of Postnikov's mixed Eulerian numbers. They arose naturally in previous work by the authors concerning the permutahedral variety and subsume well-known families of polynomials such…

We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…

We discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field $\mathbb{F}_q$. We solve this problem in the case…

Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of…