Counting set systems by weight
| dc.creator | Klazar, Martin | |
| dc.date | 2004-04-11 | |
| dc.date.accessioned | 2026-07-07T05:07:21Z | |
| dc.date.available | 2026-07-07T05:07:21Z | |
| dc.description | Applying the enumeration of sparse set partitions, we show that the number of set systems H such that the emptyset is not in H, the total cardinality of edges in H is n, and the vertex set of H is {1, 2, ..., m}, equals (1/log(2)+o(1))^nb_n where b_n is the n-th Bell number. The same asymptotics holds if H may be a multiset. If vertex degrees in H are restricted to be at most k, the asymptotics is (1/alpha_k+o(1))^nb_n where alpha_k is the unique root of x^k/k!+...+x^1/1!-1 in (0,1]. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404217 | |
| dc.identifier | http://arxiv.org/abs/math/0404217 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70830 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A16, 05A18 | |
| dc.title | Counting set systems by weight | |
| dc.type | text |