Related papers: Eulerian polynomials and polynomial congruences
In this paper, we first present combinatorial proofs of a kind of expansions of the Eulerian polynomials of types A and B, and then we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the…
We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.
In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.
In this paper, we study relations among several types of Eulerian polynomials from a combinatorial viewpoint. We establish an identity between the restricted Eulerian polynomials of types $A$ and $B$. As an application, we present a…
In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is relation between Stirling and Eulerian polynomials. Can we find a new relation between…
Recently, Nunge studied Eulerian polynomials on segmented permutations, namely \emph{generalized Eulerian polynomials}, and further asked whether their coefficients form unimodal sequences. In this paper, we prove the stability of the…
The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
In this note we prove combinatorially some new formulas connecting poly-Bernoulli numbers with negative indices to Eulerian numbers.
In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.
We study the explicit formula of Euler numbers and polynomials of higher order
Article presents a short investigation into some properties of the Moser polynomials which appear in various problems from algebraic combinatorics. For instance, these polynomials can be used to solve the Generalized Moser's Problem on…
Binomial-Eulerian polynomials were introduced by Postnikov, Reiner and Williams. In this paper, properties of the binomial-Eulerian polynomials, including recurrence relations and generating functions are studied. We present three…
We introduce new recurrences for the type B and type D Eulerian polynomials, and interpret them combinatorially. These recurrences are analogous to a well-known recurrence for the type A Eulerian polynomials. We also discuss their…
Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the location and multiplicity of the real zeros of $f$ and $F$, which generalizes and unifies many known results, including the…
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
We define a generalization of the Eulerian polynomials and the Eulerian numbers by considering a descent statistic on segmented permutations coming from the study of 2-species exclusion processes and a change of basis in a Hopf algebra. We…