The cycle descent statistic on permutations
Jun Ma, Shimei Ma, Yeong-Nan Yeh, Zhu Xu
TL;DR
This paper investigates the cycle descent statistic in permutations, introducing involutions and a bijection to Callan perfect matchings, advancing combinatorial understanding of permutation structures.
Contribution
It presents new involutions and a bijection linking negative cycle descent permutations to Callan perfect matchings, enhancing combinatorial analysis.
Findings
Constructed involutions on permutations and derangements.
Established a bijection between negative cycle descent permutations and Callan perfect matchings.
Provided new combinatorial tools for analyzing permutation statistics.
Abstract
In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Bayesian Methods and Mixture Models · Advanced Mathematical Identities