Bulletin of the Australian Mathematical Society

Table of Contents - June 2012 - Volume 85, Issue 03  

Research Article

COUNTING PERMUTATIONS BY NUMBERS OF EXCEDANCES, FIXED POINTS AND CYCLES

SHI-MEI MAa1

a1 Department of Information and Computing Science, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei 066004, PR China (email: shimeima@yahoo.com.cn)

Abstract

In this paper we present a combinatorial proof of an identity involving the two kinds of Stirling numbers and the numbers of permutations with prescribed numbers of excedances and cycles. Several recurrence relations related to the numbers of excedances, fixed points and cycles are also obtained.

(Received June 09 2011)

2010 Mathematics subject classification

  • primary 05A15; secondary 05A19

Keywords and phrases

  • excedances;
  • fixed points;
  • cycles;
  • permutations

Footnotes

This work was supported by the Fundamental Research Funds for the Central Universities (N100323013).