On the Numbers of Orbits of Permutations under an Operator Related to Eulerian Numbers

Shinji Tanimoto

Department of Mathematics, Kochi Joshi University, Kochi 780-8515, Japan

tanimoto@cc.kochi-wu.ac.jp

Annals of Combinatorics 8 (2) p.239-250 June, 2004

Abstract:

In two previous papers an operator on permutations was introduced and its applications to Eulerian numbers were discussed by means of periods and orbits under the operator. In this paper, observing particular subsequences of permutations, an explicit formula for the number of orbits is given for each period. Several identities concerning the number of orbits and its related numbers are also derived.

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