ﻻ يوجد ملخص باللغة العربية
In this paper we present grammatical interpretations of the alternating Eulerian polynomials of types A and B. As applications, we derive several properties of the type B alternating Eulerian polynomials, including combinatorial expansions, recurrence relations and generating functions. We establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials of permutations in the symmetric group, which implies that the type B alternating Eulerian polynomials have gamma-vectors alternate in sign.
A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. The aim of this paper is to establish the cycle analogue of Stembridges formula by using cycle peaks and exce
We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of polynomial
In this paper, we study Eulerian polynomials for permutations and signed permutations of the multiset ${1,1,2,2,ldots,n,n}$. Properties of these polynomials, including recurrence relations and unimodality are discussed. In particular, we give a unifi
The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on permutations are unimodal via a five-term recurrence relation. We also found a qua