Related papers: Recurrences for Eulerian polynomials of type B and…
We introduce sub-Eulerian polynomials to count elements of $D_n$ by which a recurrence relation for the Eulerian polynomials of type $D$ is obtained.
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…
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 a new array of type $D$ Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation, Worpitzky formula and the generating function. We also find the probability…
We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.
Based on the Hermite--Biehler theorem, we simultaneously prove the real-rootedness of Eulerian polynomials of type $D$ and the real-rootedness of affine Eulerian polynomials of type $B$, which were first obtained by Savage and Visontai by…
In this paper, we establish a connection between the 1/k-Eulerian polynomials introduced by Savage and Viswanathan (Electron. J. Combin. 19(2012), P9) and k-Stirling permutations. We also introduce the dual set of Stirling permutations.
We use the method of mutual interlacing to prove two conjectures on the real-rootedness of Eulerian-like polynomials: Brenti's conjecture on $q$-Eulerian polynomials for Weyl groups of type $D$, and Dilks, Petersen, and Stembridge's…
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 prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.
In this paper, we characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems, which generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including flag descent…
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…
A remarkable identity involving the Eulerian polynomials of type D was obtained by Stembridge (Adv. Math. 106 (1994), p. 280, Lemma 9.1). In this paper we explore an equivalent form of this identity. We prove Brenti's real-rootedness…
In this paper, we give a type B analogue of the 1/k-Eulerian polynomials. Properties of this kind of polynomials, including combinatorial interpretations, recurrence relations and gamma-positivity are studied. In particular, we show that…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the…
In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.
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,…
The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…
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…