Counting and Computing by $e$
| dc.creator | Hassani, Mehdi | |
| dc.date | 2006-06-26 | |
| dc.date.accessioned | 2026-07-07T07:17:39Z | |
| dc.date.available | 2026-07-07T07:17:39Z | |
| dc.description | In this paper we count the number of paths and cycles in complete graphs by using the number $e$. Also, we compute the number of derangements in same way. Connection by $e$ yields some nice formulas for the number of derangements, such as $D_n=\lfloor\frac{n!+1}{e}\rfloor$ and $D_n=\lfloor(e+e^{-1})n!\rfloor-\lfloor en!\rfloor$, and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; these connections are hidden in the heart of a nice polynomial that we call it derangement function and a simple ordinary differential equation concerning it. | |
| dc.description | 12 pages, no figure, review of my works about the number of derangements | |
| dc.identifier | https://arxiv.org/abs/math/0606613 | |
| dc.identifier | http://arxiv.org/abs/math/0606613 | |
| dc.identifier | M. Hassani, Derangements and Applications, Journal of Integer Sequences (JIS), Volume 6, Issue 1, Article 03.1.2, 2003. M. Hassani, Cycles in graphs and derangements, Math. Gaz. 88 (March 2004) pp. 123-126 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114014 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 40A25, 05C17, 05C38, 65L99, 33B20, 33C20, 26D15, 11J72, 20B40 | |
| dc.title | Counting and Computing by $e$ | |
| dc.type | text |