Search
Search Results
-
Balanced Stirling numbers
Hsu and Shiue (Adv Appl Math 20(3):366–384, 1998. https://doi.org/10.1006/aama.1998.0586 ) defined generalized Stirling numbers, which include as...
-
Some identities and properties on degenerate Stirling numbers
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the...
-
Generalizations of Stirling-like and Bell-like Numbers
Stirling and Bell numbers play a fundamental role in enumerative combinatorics, they count, among others, partitions of a finite set. We give a...
-
On q-generalized (r, s)-Stirling numbers
In this paper by using q -numbers and r -shift, the ( q , r )-Stirling numbers with level s are studied. One of the main aims is to give several...
-
Congruence relation between Stirling numbers of the first and second kinds
This paper consists of certain congruence properties of Stirling numbers of the first and second kinds. Some congruence relations between s ( n , k ) and S (...
-
Multi-Lah numbers and multi-Stirling numbers of the first kind
In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose...
-
Some Positivities in Stirling Arrays with Higher Level
In this paper, we prove that the sequences of the Stirling numbers of the first and second kind with higher level are both Pólya frequency and...
-
Recurrence Relations of Poly-Cauchy Numbers by the r-Stirling Transform
We give some formulas of poly-Cauchy numbers by the r -Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are...
-
New Modular Symmetric Function and its Applications: Modular s-Stirling Numbers
In this paper, we consider generalizations of the Stirling number of the first and the second kind by using a specialization of a new family of...
-
Multipermutations and Stirling Multipermutations
We consider multipermutations and a certain partial order, the weak Bruhat order, on this set. This generalizes the Bruhat order for permutations,...
-
Bernoulli numbers with level 2
Stirling numbers with higher level may be considered to have been introduced by Tweedie (Proc Edinb Math Soc 37:2–25, 1918). These numbers have been...
-
Stirling complexes
In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number of resources to labeled nodes of a...
-
Construction and computation of unified Stirling-type numbers emerging from p-adic integrals and symmetric polynomials
The aim of this paper is to give construction and computation methods for generalized and unified representations of Stirling-type numbers and...
-
-
A note on degenerate r-Stirling numbers
The aim of this paper is to study the unsigned degenerate r -Stirling numbers of the first kind as degenerate versions of the r -Stirling numbers of...
-
On some congruences of sums of powers and Wolstenholme’s theorem for generalized harmonic numbers
In this paper, we first attempt to study sums of powers and to obtain some divisibility properties of the Stirling numbers of the first kind based on...