Classifying Descents According to Parity |
| |
| Authors: | Sergey Kitaev Jeffrey Remmel |
| |
| Affiliation: | (1) Institute of Mathematics, Reykjavík University, IS-103 Reykjavík, Iceland;(2) Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA |
| |
| Abstract: | In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results. Received September 7, 2005 |
| |
| Keywords: | permutation statistics descents parity distribution bijection |
| 本文献已被 SpringerLink 等数据库收录！ |
|
