Riffle shuffles,cycles, and descents |
| |
| Authors: | Persi Diaconis Michael Mc Grath Jim Pitman |
| |
| Institution: | (1) Dept. of Mathematics, Harvard University, 02138 Cambridge, MA;(2) 410B2 Cirrus Logic 3100 West Warren Avenue, 94358 Fremont, CA;(3) Dept. of Statistics, University of California, 94720 Berkeley, CA |
| |
| Abstract: | We derive closed form expressions and limiting formulae for a variety of functions of a permutation resulting from repeated
riffle shuffles. The results allow new formulae and approximations for the number of permutations inS
n with given cycle type and number of descents. The theorems are derived from a bijection discovered by Gessel. A self-contained
proof of Gessel's result is given. |
| |
| Keywords: | 05 A 15 60 C 05 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
