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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