Sign imbalances of snakes and valley-signed permutations

Huilan Chang, Sen-Peng Eu, Yuan Hsun Lo

Research output: Contribution to journalArticle

Abstract

One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type An is the set of the alternating permutations and in type Bn (or Dn) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Vergès, Novelli and Thibon, is another structure counted by the Springer numbers of type Bn (or Dn). In this paper we determine the sign imbalances of these sets of snakes and valley-signed permutations under various inversion statistics invw, inv o, invs, invB, and invD.

Original languageEnglish
Pages (from-to)26-47
Number of pages22
JournalAdvances in Applied Mathematics
Volume59
DOIs
Publication statusPublished - 2014 Jan 1

Keywords

  • Alternating permutation
  • Inversions
  • Sign imbalance
  • Snake
  • Valley-signed permutation

ASJC Scopus subject areas

  • Applied Mathematics

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