Cyclically consecutive permutation avoidance

Research output: Contribution to journalArticlepeer-review


We give an explicit formula for the number of permutations that cyclically avoid a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in οn is given by n! times the convergent series Σk=-∞ (3/2φ(k+1/3)n for n ≤ 2.

Original languageEnglish
Pages (from-to)1385-1390
Number of pages6
JournalSIAM Journal on Discrete Mathematics
Issue number3
StatePublished - 2016

Bibliographical note

Publisher Copyright:
Copyright © by SIAM.


  • Cyclic consecutive pattern avoidance
  • Integral operators
  • Spectrum
  • Trace class operators

ASJC Scopus subject areas

  • General Mathematics


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