Related papers: Cumulants and convolutions via Abel polynomials
The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…
Spivey found a recurrence relation for the Bell numbers by using combinatorial method. The aim of this paper is to derive Spivey's type recurrence relations for the degenerate Bell polynomials and the degenerate Dowling polynomials by using…
In the context of the Batalin-Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander-Conway polynomial. The three-dimensional case is analyzed explicitly, and…
Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cayley permutation is a word of positive integers such that if…
We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of exponential sums associated to different…
Initiated by a result of Gorin and Marcus [Int. Math. Res. Not., (3):883--913, 2020] and an observation of Steinerberger [Proc. Amer. Math. Soc., 147(11):4733--4744, 2019], there has been a recent growing body of literature connecting…
Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial…
In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…
The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial properties. We give several different formulas for these polynomials. We also study a more…
Gaussian binomial coefficients are q-analogues of the binomial coefficients of integers. On the other hand, binomial coefficients have been extended to finite words, i.e., elements of the finitely generated free monoids. In this paper we…
A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number--theoretical properties. A new class of…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
Recently, in a work that grew out of their exploration of interlacing polynomials, Marcus, Spielman and Srivastava and then Marcus studied certain combinatorial polynomial convolutions. These convolutions preserve real-rootedness and…
We show how Wick polynomials of random variables can be defined combinatorially as the unique choice which removes all "internal contractions" from the related cumulant expansions, also in a non-Gaussian case. We discuss how an expansion in…
In this paper special values of Bell polynomials are given by using the power series solution of the equation $y^{(k)}=e^{ay}$. In addition, complete and partial exponential autonomous functions, exponential autonomous polynomials,…
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
In this paper we characterize local exponential monomials and polynomials on different types of Abelian groups and we prove Montel-type theorems for these function classes.
We provide several simple recursive formulae for the moment sequence of infinite Bernoulli convolution. We relate moments of one infinite Bernoulli convolution with others having different but related parameters. We give examples relating…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…