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 relationship to polynomials introduced by Savage and Visontai in connection to the real-rootedness of the corresponding Eulerian polynomials.

Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.

Based Based on on two two inversion inversion formulas formulas for for enumerating enumerating words words in in the the free free monoid monoid by by adjacencies, adjacencies, we we present present a a new new approach approach to to a a class class of of permutation permutation problems problems having having Eulerian-type Eulerian-type generating generating functions. functions. We We also ...

An even-cycle decomposition of a graph G is a partition of E(G) into cycles of even length. Evidently, every Eulerian bipartite graph has an even-cycle decomposition. Seymour (1981) proved that every 2-connected loopless Eulerian planar graph with an even number of edges also admits an even-cycle decomposition. Later, Zhang (1994) generalized this to graphs with no K5-minor. Our main theorem gi...

Recent years have witnessed significant improvements in the computer modeling of fluidized particle systems. Such models hold the potential to simulate complex systems and thus greatly reduce design efforts. As we approach the goal of simulating arbitrary systems, there exists a greater need to challenge the ability of the models to predict key features of operating beds. The simplest challenge...

Abstract 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 coefficients of descent polynomials D d (t) are logconcave. This paper also provides a new approach to study Eulerian numbers and descent polynomials.

The Stochastic Eulerian Tour Problem was introduced in 2008 [1] as a stochastic variant of the well-known Eulerian Tour Problem. In a follow-up paper the same authors investigated some heuristics for solving the Stochastic Eulerian Tour Problem [2]. After a thorough study of these two publications a few issues emerged. In this short research commentary we would like to discuss these issues. For...

A 2-cell embedding of an Eulerian digraph in a closed surface is said to be directed if the boundary of each face is a directed closed walk in G. We prove Kuratowski-type theorems about obstructions to directed embeddings of Eulerian digraphs in the plane.

A graph (digraph) G = (V,E) with a set T ⊆ V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky [1] and Lovász [15] showed that the maximum number of pairwise edge-disjoint T -paths in an inner Eulerian graph G is equal to 1 2 ∑ s∈T λ(s), where λ(s) is the minimum number of edges whose remova...