On a question of Li concerning an uncounted class of circular permutations

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, we find an explicit formula for the generating function that counts the circular permutations of length n avoiding the pattern 2341, whose enumeration was raised as an open problem by Rupert Li. This then completes in all cases the enumeration of circular permutations that avoid a single vincular pattern of length four containing one vincu-lum. To establish our results, we introduce three auxiliary arrays which when taken together refine the cardinality of the class of permutations in question. Rewriting the recurrences of these arrays in terms of generating functions leads to functional equations which are solved by various means including the kernel method and iteration.

Original languageEnglish
Pages (from-to)176-195
Number of pages20
JournalAustralasian Journal of Combinatorics
Issue number1
StatePublished - Jun 2022

Bibliographical note

Publisher Copyright:
©The author(s). Released under the CC BY 4.0 International License.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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