Séminaire Lotharingien de Combinatoire, 86B.17 (2022), 12 pp.
Bin Han, Jianxi Mao and Jiang Zeng
Equidistributions Around Special Kinds of Descents and Excedances Via Continued Fractions
Abstract.
We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials.
Using the combinatorial theory of Jacobi-type continued fractions and bijections we derive various combinatorial interpretations in terms of permutation statistics for these polynomials, which include
special kinds of descents and excedances in a recent paper of
Baril and Kirgizov. As a by-product, we derive several equidistribution results for permutation statistics, which enables us to
confirm and strengthen a recent conjecture of Vajnovszki and also to obtain
several companion permutation statistics for
two bistatistics in a conjecture of Baril and Kirgizov.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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