The r-Stifling numbers of the first and second kind count restricted permutations and respectively restricted partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic properties of these numbers, which i
Stirling numbers revisited
โ Scribed by Raymond Scurr; Gloria Olive
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 527 KB
- Volume
- 189
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
extended from N* to Z*. These extensions lead to Laurent series, 'special branches', and interesting formulas (including the 'Stirling Duality Law'). @
๐ SIMILAR VOLUMES
We define the degenerate weighted Stifling numbers of the first and second kinds, Sl(n, k, 2t ] 0) and S(n, k, )t ] O). By specializing h and 0 we can obtain the Stirling numbers, the weighted Stifling numbers and the degenerate Stifling numbers. Basic properties of Sl(n, k, h { 0) and S(n, k, ;t I
The theory of modular binomial lattices enables the simultaneous combinatorial analysis of finite sets, vector spaces, and chains. Within this theory three generalizations of Stifling numbers of the second kind, and of Lah numbers, are developed.
This paper presents some relationships between Pascal matrices, Stirling numbers, and Bernouilli numbers.