Counting derangements with signed right-to-left minima and excedances

Yanni Pei (1) , Jiang Zeng (2, 3)

1 China Three Gorges University
2 CTN - Combinatoire, théorie des nombres
3 ICJ - Institut Camille Jordan

Recently Alexandersson and Getachew proved some multivariate generalizations of a formula for enumerating signed excedances in derangements. In this paper we first relate their work to a recent continued fraction for permutations and confirm some of their observations. Our second main result is two refinements of their multivariate identities, which clearly explain the meaning of each term in their main formulas. We also explore some similar formulas for permutations of type B.

Domaines: Mathématiques [math]

Yanni Pei, Jiang Zeng. Counting derangements with signed right-to-left minima and excedances. Advances in Applied Mathematics, 2024, 152, pp.102599. ⟨10.1016/j.aam.2023.102599⟩. ⟨hal-04442944⟩