Parity statistics on restricted permutations and the Catalan--Schett polynomials
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929483834982400 |
|---|---|
| author | Lin, Zhicong Liu, Jing Yan, Sherry H. F. |
| author_facet | Lin, Zhicong Liu, Jing Yan, Sherry H. F. |
| contents | Motivated by Kitaev and Zhang's recent work on non-overlapping ascents in stack-sortable permutations and Dumont's permutation interpretation of the Jacobi elliptic functions, we investigate some parity statistics on restricted permutations. Some new related bijections are constructed and two refinements of the generating function for descents over $321$-avoiding permutations due to Barnabei, Bonetti and Silimbanian are obtained. In particular, an open problem of Kitaev and Zhang about non-overlapping ascents on $321$-avoiding permutations is solved and several combinatorial interpretations for the Catalan--Schett polynomials are found. The stack-sortable permutations are at the heart of our approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parity statistics on restricted permutations and the Catalan--Schett polynomials Lin, Zhicong Liu, Jing Yan, Sherry H. F. Combinatorics Motivated by Kitaev and Zhang's recent work on non-overlapping ascents in stack-sortable permutations and Dumont's permutation interpretation of the Jacobi elliptic functions, we investigate some parity statistics on restricted permutations. Some new related bijections are constructed and two refinements of the generating function for descents over $321$-avoiding permutations due to Barnabei, Bonetti and Silimbanian are obtained. In particular, an open problem of Kitaev and Zhang about non-overlapping ascents on $321$-avoiding permutations is solved and several combinatorial interpretations for the Catalan--Schett polynomials are found. The stack-sortable permutations are at the heart of our approaches. |
| title | Parity statistics on restricted permutations and the Catalan--Schett polynomials |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.01558 |