Counting covered fixed points and covered arcs in an involution

Ronit Mansour

Research output: Contribution to journalArticlepeer-review

Abstract

An involution on [n] = {1, 2,…, n} is a permutation π 1 π 2… πn on [n] such that π πi = i for all i ∈ [n]. Let π = π 1 π 2 n be any involution on [n]. We say that i is a covered fixed point of π if π i = i and there exists a, b such that 1 ≤ a < i < b ≤ n and π a = b. We say that ab is a covered arc of π if there exists c, d such that 1 ≤ c < a < b < d ≤ n, π a = b, and π c = d. In this paper, we study the generating function for the number of involutions on [n] according to the number of covered fixed points/covered arcs.

Original languageEnglish
Pages (from-to)2625-2635
Number of pages11
JournalQuaestiones Mathematicae
Volume46
Issue number12
DOIs
StatePublished - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 NISC (Pty) Ltd.

Keywords

  • covered arcs
  • covered fixed points
  • Lined patterns

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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