A Bijection Between All Shi Regions and Core Partitions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929512439087104 |
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| author | Davis, Matthew |
| author_facet | Davis, Matthew |
| contents | We extend the bijection of Fishel-Vazirani on dominant regions of the $m$-Shi arrangement. Our map puts the set of all minimal chambers of the $m$-Shi arrangement of Type $A_{n}$ in bijection with a certain set of (equivalence classes of) $n$-core partitions. As a step to our proof, we give a potentially interesting classification of the alcoves in the $S_{n}$-orbit of an $m$-minimal alcove which are themselves $m$-minimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Bijection Between All Shi Regions and Core Partitions Davis, Matthew Combinatorics Representation Theory 05E10 (Primary) 52C35 (Secondary) We extend the bijection of Fishel-Vazirani on dominant regions of the $m$-Shi arrangement. Our map puts the set of all minimal chambers of the $m$-Shi arrangement of Type $A_{n}$ in bijection with a certain set of (equivalence classes of) $n$-core partitions. As a step to our proof, we give a potentially interesting classification of the alcoves in the $S_{n}$-orbit of an $m$-minimal alcove which are themselves $m$-minimal. |
| title | A Bijection Between All Shi Regions and Core Partitions |
| topic | Combinatorics Representation Theory 05E10 (Primary) 52C35 (Secondary) |
| url | https://arxiv.org/abs/2409.15659 |