Refined Eulerian numbers and ballot permutations

We present computer-generated proofs for some summation identities for ($q$-)Stirling and ($q$-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number identities with a recurrence solver for difference fields.

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New Eulerian Numbers of Type $D$

The Electronic Journal of Combinatorics ◽

10.37236/5514 ◽

2016 ◽

Vol 23 (1) ◽

Cited By ~ 1

Author(s):

Anna Borowiec ◽

Wojciech Młotkowski

Keyword(s):

Recurrence Relation ◽

Generating Function ◽

Probability Distributions ◽

Type A ◽

Eulerian Numbers ◽

Eulerian Polynomials ◽

Type D

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 distributions whose moments are Eulerian polynomials of type $A$, $B$ and $D$.

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Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps

Fractional Differential Equations ◽

10.1515/9783110571660-003 ◽

2019 ◽

pp. 47-64 ◽

Cited By ~ 1

Author(s):

Mark Edelman

Keyword(s):

Power Law ◽

Fractional Difference ◽

Direct Introduction ◽

Eulerian Numbers

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Beyond the Euler summation formula

The Mathematical Gazette ◽

10.1017/s0025557200176065 ◽

2004 ◽

Vol 88 (513) ◽

pp. 432-440 ◽

Cited By ~ 1

Author(s):

Barry Lewis

Keyword(s):

Summation Formula ◽

Eulerian Numbers ◽

The Subject ◽

Established Technique

The Eulerian numbers are not strangers to readers of the Gazette but they are not normally associated with the subject of this article, despite the similarity of their names. This article seeks to use Eulerian numbers in generalised telescoping sums, a role that is a powerful extension of an established technique – the Euler summation formula.

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On Fully Degenerate Daehee Numbers and Polynomials of the Second Kind

Journal of Mathematics ◽

10.1155/2020/7893498 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Sang Jo Yun ◽

Jin-Woo Park

Keyword(s):

Exponential Function ◽

Special Functions ◽

Eulerian Numbers

In a study, Carlitz introduced the degenerate exponential function and applied that function to Bernoulli and Eulerian numbers and degenerate special functions have been studied by many researchers. In this paper, we define the fully degenerate Daehee polynomials of the second kind which are different from other degenerate Daehee polynomials and derive some new and interesting identities and properties of those polynomials.

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