Involutions containing exactly r pairs of intersecting arcs

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The generating function Fr(x) that counts the involutions on n letters containing exactly r pairs of intersecting arcs in their graphical representation is studied. More precisely, an algorithm that computes the generating function Fr(x) for any given r ≥ 0 is presented. To derive the result for a given r, the algorithm performs certain routine checks on involutions of length 2r + 2 without fixed points. The algorithm is implemented in Maple and yields explicit formulas for 0 ≤ r ≤ 4.

Original languageEnglish
Pages (from-to)64-67
Number of pages4
JournalDiscrete Mathematics Letters
StatePublished - 2022

Bibliographical note

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© 2022 the author.


  • arc-pattern 3412
  • involution

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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