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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.17670 |
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| _version_ | 1866913998765555712 |
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| author | Aharoni, Ron Berger, Eli Guo, He Kotlar, Daniel |
| author_facet | Aharoni, Ron Berger, Eli Guo, He Kotlar, Daniel |
| contents | A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is filled injectively with the numbers $1, \ldots ,a_i$, where $a_i$ is the length of $i$th row of $Y$, and every column is also filled injectively. A conjecture of Chow and Taylor, publicized by Chow, Fan, Goemans, and Vondrak is that a wide Young diagram is Latin. We prove a dual version of the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17670 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 2-covers of wide Young diagrams Aharoni, Ron Berger, Eli Guo, He Kotlar, Daniel Combinatorics Discrete Mathematics 05A17, 05C65, 05C70, 05D15 A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is filled injectively with the numbers $1, \ldots ,a_i$, where $a_i$ is the length of $i$th row of $Y$, and every column is also filled injectively. A conjecture of Chow and Taylor, publicized by Chow, Fan, Goemans, and Vondrak is that a wide Young diagram is Latin. We prove a dual version of the conjecture. |
| title | 2-covers of wide Young diagrams |
| topic | Combinatorics Discrete Mathematics 05A17, 05C65, 05C70, 05D15 |
| url | https://arxiv.org/abs/2311.17670 |