Consecutive and quasi-consecutive patterns : des-Wilf classifications and generating functions

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Fang, Qi and Fu, Shishuo and Kitaev, Sergey and Li, Haijun and Wang, Yan (2026) Consecutive and quasi-consecutive patterns : des-Wilf classifications and generating functions. Journal of Combinatorics. ISSN 2156-3527 (In Press)

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Abstract

Motivated by a correlation between the distribution of descents over permutations that avoid a consecutive pattern and those avoiding the respective quasi-consecutive pattern, as established in this paper, we obtain a complete des-Wilf classification for quasi-consecutive patterns of length up to 4. For equivalence classes containing more than one pattern, we construct various descent-preserving bijections to establish the equivalences, which lead to the provision of proper versions of two incomplete bijective arguments previously published in the literature. Additionally, for two singleton classes, we derive explicit bivariate generating functions using the generalized run theorem.

ORCID iDs

Fang, Qi, Fu, Shishuo, Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647, Li, Haijun and Wang, Yan;
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