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| Auteurs principaux: | , |
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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2406.10927 |
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| _version_ | 1866910489104089088 |
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| author | Choi, Yunseo Gan, Katelyn |
| author_facet | Choi, Yunseo Gan, Katelyn |
| contents | In 2023, Defant and Li introduced the Ungar move, which sends an element $v$ of a finite meet-semilattice $L$ to the meet of some subset of the elements covered by $v$. More recently, Defant, Kravitz, and Williams introduced the Ungar game on $L$, in which two players take turns making Ungar moves starting from an element of $L$ until the player that cannot make a nontrivial Ungar move loses. In this note, we settle two conjectures by Defant, Kravitz, and Williams on the Ungar games on the Young-Fibonacci lattice and the lattices of the order ideals of shifted staircases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ungar Games on the Young-Fibonacci and the Shifted Staircase Lattices Choi, Yunseo Gan, Katelyn Combinatorics In 2023, Defant and Li introduced the Ungar move, which sends an element $v$ of a finite meet-semilattice $L$ to the meet of some subset of the elements covered by $v$. More recently, Defant, Kravitz, and Williams introduced the Ungar game on $L$, in which two players take turns making Ungar moves starting from an element of $L$ until the player that cannot make a nontrivial Ungar move loses. In this note, we settle two conjectures by Defant, Kravitz, and Williams on the Ungar games on the Young-Fibonacci lattice and the lattices of the order ideals of shifted staircases. |
| title | Ungar Games on the Young-Fibonacci and the Shifted Staircase Lattices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.10927 |