Descent classes of permutations with a given number of fixed points

Jacques Désarménien, Michelle L. Wachs

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24 Scopus citations

Abstract

A desarrangement is a permutation whose first ascent is even. The first author introduced this class of permutations for the purpose of combinatorially explaining a standard recurrence relation for the number of derangements of n elements. He gave a nice bijection between derangements and desarrangements. Here we extend his bijection to obtain more refined enumeration results relating derangements and desarrangements. In particular, we construct a bijection between descent classes of derangements and descent classes of desarrangements. The following monotonicity result is a consequence of this correspondence: In any (nontrivial) descent class the number of permutations with exactly k fixed points decreases as k increases.

Original languageEnglish (US)
Pages (from-to)311-328
Number of pages18
JournalJournal of Combinatorial Theory, Series A
Volume64
Issue number2
DOIs
StatePublished - Jan 1 1993

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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