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Results tagged with co.combinatorics
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user 174295
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
4
votes
1
answer
296
views
How are the Eulerian numbers of the first-order related to the Eulerian numbers of the secon...
The question is inspired by G. Rzadkowski and M. Urlinska's examples in their paper A Generalization of the Eulerian Numbers. They refer to the discussion
Expressions involving Eulerian numbers of the …
- 251
0
votes
Accepted
How are the Eulerian numbers of the first-order related to the Eulerian numbers of the secon...
The identity is valid. This is a corollary to a proof of Amy M. Fu, Some Identities Related to the Second-Order Eulerian Numbers.
A second proof follows from recent work of Cormac O'Sullivan, Stirling …
- 251
2
votes
The factorials of -1, -2, -3, …
Hadrian Ulgenes David Peter give the following answer in
Series and Product Representations of Gamma and Pseudogamma Functions, Theorem 5:
The function
\begin{equation}
\Lambda(x)=\prod_{n=1}^{\infty} …
- 251
4
votes
0
answers
124
views
A combinatorial triangle for the Bernoulli numbers
Motivation: We informally call an infinite lower triangular matrix
$\operatorname{T}(n, k)$ of integers a combinatorial triangle of a sequence of integers or
rational numbers if it can be obtained fro …
- 251
5
votes
0
answers
186
views
The existence of $n$-sided cells in regular $m$-gons
For any integer $n >= 3$, does there exist a regular
$m$-gon with all diagonals drawn containing a cell with $n$ sides?
See A342222 and its cross-references.
Regular polygon on the Wiki.
…
- 251