Inversion sequences and signed permutations

Toufik Mansour, Amir Safadi

Research output: Contribution to journalArticlepeer-review

Abstract

A signed inversion sequence of length n is a sequence of integers (Formula Present), where (Formula Present) for every i ∈ {0, 1, …, n − 1}. For a set of signed patterns B, let Īn(B) be the set of signed inversion sequences of length n that avoid all the signed patterns from B. We say that two sets of signed patterns B and C are Wilf-equivalent if |Īn(B)| = |Īn(C)| for every n ≥ 0. In this paper, by generating trees, we show that the number of Wilf-equivalences among singles of a length-2 signed pattern is 3 and the number of Wilf-equivalences among pairs of a length-2 signed patterns is 30.

Original languageEnglish
Pages (from-to)13-20
Number of pages8
JournalDiscrete Mathematics Letters
Volume14
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 the authors.

Keywords

  • generating trees
  • inversion sequences
  • signed inversion sequences
  • Wilf-equivalences

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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