Tilings of Benzels via the Abacus Bijection
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913961003188224 |
|---|---|
| author | Defant, Colin Li, Rupert Propp, James Young, Benjamin |
| author_facet | Defant, Colin Li, Rupert Propp, James Young, Benjamin |
| contents | Propp recently introduced regions in the hexagonal grid called benzels and stated several enumerative conjectures about the tilings of benzels using two types of prototiles called stones and bones. We resolve two of his conjectures and prove some additional results that he left tacit. In order to solve these problems, we first transfer benzels into the square grid. One of our primary tools, which we combine with several new ideas, is a bijection (rediscovered by Stanton and White and often attributed to them although it is considerably older) between $k$-ribbon tableaux of certain skew shapes and certain $k$-tuples of Young tableaux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05717 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tilings of Benzels via the Abacus Bijection Defant, Colin Li, Rupert Propp, James Young, Benjamin Combinatorics 05B45, 05A15, 05A17 Propp recently introduced regions in the hexagonal grid called benzels and stated several enumerative conjectures about the tilings of benzels using two types of prototiles called stones and bones. We resolve two of his conjectures and prove some additional results that he left tacit. In order to solve these problems, we first transfer benzels into the square grid. One of our primary tools, which we combine with several new ideas, is a bijection (rediscovered by Stanton and White and often attributed to them although it is considerably older) between $k$-ribbon tableaux of certain skew shapes and certain $k$-tuples of Young tableaux. |
| title | Tilings of Benzels via the Abacus Bijection |
| topic | Combinatorics 05B45, 05A15, 05A17 |
| url | https://arxiv.org/abs/2209.05717 |