Combinatorial proofs of inverse relations and log-concavity for Bessel numbers
| dc.creator | Han, Hyuk | |
| dc.creator | Seo, Seunghyun | |
| dc.date | 2004-06-18 | |
| dc.date | 2004-06-20 | |
| dc.date.accessioned | 2026-07-07T05:09:22Z | |
| dc.date.available | 2026-07-07T05:09:22Z | |
| dc.description | Let the Bessel number of the second kind B(n,k) be the number of set partitions of [n] into k blocks of size one or two, and let the Bessel number of the first kind b(n,k) be a certain coefficient in n-th Bessel polynomial. In this paper, we show that Bessel numbers satisfy two properties of Stirling numbers: The two kinds of Bessel numbers are related by inverse formulas, and both Bessel numbers of the first kind and the second kind form log-concave sequences. By constructing sign-reversing involutions, we prove the inverse formulas. We review Krattenthaler's injection for the log-concavity of Bessel numbers of the second kind, and give a new explicit injection for the log-concavity of signless Bessel numbers of the first kind. | |
| dc.description | 9 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0406378 | |
| dc.identifier | http://arxiv.org/abs/math/0406378 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71607 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 (Primary) 05A19, 05A20, 05C70 (Secondary) | |
| dc.title | Combinatorial proofs of inverse relations and log-concavity for Bessel numbers | |
| dc.type | text |