相关论文: Some multivariate master polynomials for permutati…
We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…
We study generating functions for the number of permutations in $S_n$ subject to set of restrictions. One of the restrictions belongs to $S_3$, while the others to $S_k$. It turns out that in a large variety of cases the answer can be…
We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables:…
We present a decomposition of the generalized binomial coefficients associated with Jack polynomials into two factors: a stem, which is described explicitly in terms of hooks of the indexing partitions, and a leaf, which inherits various…
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
In this paper we describe the group of symmetries of a two-dimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: the Dirichlet-type…
We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian…
In this paper, we introduce the notion of the complete joint Jacobi polynomial of two linear codes of length $n$ over $\mathbb{F}_q$ and $\mathbb{Z}_k$. We give the MacWilliams type identity for the complete joint Jacobi polynomials of…
We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…
We present new classes of permutation polynomials over finite fields.
We relate hook-length products for adjacent staircase partitions to special values of Jacobi polynomials. This connection expresses the number of semistandard tableaux in terms of Jacobi polynomials defined via Gauss hypergeometric…
A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
By using Schur transformed sequences and Dyukarev-Stieltjes parameters we obtain a new representation of the resolvent matrix corresponding to the truncated matricial Stieltjes moment problem. Explicit relations between orthogonal matrix…
We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.
The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be…