Name
Abstract | ||
|---|---|---|
The Stirling numbers of the second kind nk (counting the number of partitions of a set of size n into k non-empty classes) satisfy the relation (xD)nf(x)=∑k≥0nkxkDkf(x) where f is an arbitrary function and D is differentiation with respect to x. More generally, for every word w in alphabet {x,D} the identity wf(x)=x(#(x’s in w)−#(D’s in w))∑k≥0Sw(k)xkDkf(x) defines a sequence (Sw(k))k of Stirling numbers (of the second kind) of w. Explicit expressions for, and identities satisfied by, the Sw(k) have been obtained by numerous authors, and combinatorial interpretations have been presented. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.ejc.2014.07.002 | European Journal of Combinatorics |
DocType | Volume | Issue |
Journal | 43 | C |
ISSN | Citations | PageRank |
0195-6698 | 3 | 1.36 |
References | Authors | |
4 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| John Engbers | 1 | 21 | 6.79 |
| David Galvin | 2 | 55 | 11.59 |
| Justin Hilyard | 3 | 3 | 1.36 |