Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients
| dc.creator | Dziemianczuk, M. | |
| dc.date | 2009-01-11 | |
| dc.date.accessioned | 2026-07-07T12:28:16Z | |
| dc.date.available | 2026-07-07T12:28:16Z | |
| dc.description | F-nomial coefficients encompass among others well-known binomial coefficients or Gaussian coefficients that count subsets of finite set and subspaces of finite vector space respectively. Here, the so called F-cobweb tiling sequences N(a) are considered. For such specific sequences a new interpretation with respect to Kwasniewski general combinatorial interpretation of F-nomial coefficients is unearhed. Namely, for tiling sequences F = N(a)$ the F-nomial coefficients are equal to the number of labeled special bipartite multigraphs denoted here as a-multigraphs G(a,n,k). An explicit relation between the number of k-colored a-multigraphs and multi N(a)-nomial coefficients is established. We also prove that the unsigned values of the first row of inversion matrix for N(a) -nomial coefficients considered here are equal to the numbers of directed acyclic a-multigraphs with n nodes. | |
| dc.description | 11 pages, Affiliated to The Internet Gian-Carlo Polish Seminar http://ii.uwb.edu.pl/akk/sem/sem_rota.htm | |
| dc.identifier | https://arxiv.org/abs/0901.1337 | |
| dc.identifier | http://arxiv.org/abs/0901.1337 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215480 | |
| dc.subject | Combinatorics | |
| dc.title | Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients | |
| dc.type | text |