Work

A descent-excedance correspondence in colored permutation groups

Year: 2025

Type: article

Abstract: It is well known that descents and excedances are equidistributed in the symmetric group.We show that the descent and excedance enumerators, summed over permutations with a fixed first letter, are identical when we perform a simple change of the first letter.We generalize this to type B and colored permutation groups.We find q-analogues of generating functions for descent enumerating polynomials with respect to the major index when summed over permutations that start with a fixed first letter.Using the flag major index, we also generalise to obtain type B results.In the univariate case, we show that the aforementioned polynomials are real-rooted but need not be palindromic.Finally, we show that a symmetrised descent enumerating polynomial over the hyperoctahedral group with fixed first letter is palindromic and gamma-positive.

Source: Enumerative Combinatorics and Applications

DOI: 10.54550/eca2025v5s3r24

Authors: Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian

Institutions: Indian Institute of Science Education and Research Kolkata, Indian Institute of Technology Bombay

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Department of Science and Technology, Ministry of Science and Technology, India, National Board for Higher Mathematics

OpenAlex ID: W4414028801

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