On the descent polynomial of signed multipermutations

2013/10/24 by Zhicong Lin, Lin, Zhicong
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CO

paper · pdf · doi:10.48550/arxiv.1310.6726

8 pages

arxiv created 2013/10/24 · openalex publication_date 2013/10/24 · arxiv updated 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by a conjecture of Savage and Visontai about the equidistribution of the descent statistic on signed permutations of the multiset \1,1,2,2,…,n,n\ and the ascent statistic on (1,4,3,8,…,2n-1,4n)-inversion sequences, we investigate the descent polynomial of the signed permutations of a general multiset. We obtain a factorial generating function formula for a q-analog of these descent polynomials and apply it to show that they have only real roots. Two different proofs of the conjecture of Savage and Visontai are provided.

Citations

• q-Eulerian Polynomials Arising from Coxeter Groups
• s-Inversion Sequences and P-Partitions of Type B

Related

• The descent statistic on signed simsun permutations
• Restricted inversion polynomials
• s-Inversion Sequences and P-Partitions of Type B
• A permutation code preserving a double Eulerian bistatistic
• Descent polynomials