Abstract
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 language | English |
---|---|
Pages (from-to) | 176-195 |
Number of pages | 20 |
Journal | Australasian Journal of Combinatorics |
Volume | 83 |
Issue number | 1 |
State | Published - 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