Interval-closed set rowmotion and homomesy on products of two chains
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866908352333742080 |
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| author | Lafrenière, Nadia Lewis, Joel Brewster McNicholas, Erin Striker, Jessica Welch, Amanda |
| author_facet | Lafrenière, Nadia Lewis, Joel Brewster McNicholas, Erin Striker, Jessica Welch, Amanda |
| contents | We study rowmotion dynamics on interval-closed sets. Our first main result proves a simplification of the global definition of interval-closed set rowmotion from (Elder, Lafrenière, McNicholas, Striker, and Welch 2024). We then completely describe the orbits of interval-closed set rowmotion on products of two chains $[2]\times[n]$ and use this understanding to prove a homomesy conjecture from (ELMSW 2024) involving the signed cardinality statistic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interval-closed set rowmotion and homomesy on products of two chains Lafrenière, Nadia Lewis, Joel Brewster McNicholas, Erin Striker, Jessica Welch, Amanda Combinatorics 05E15, 06A07 We study rowmotion dynamics on interval-closed sets. Our first main result proves a simplification of the global definition of interval-closed set rowmotion from (Elder, Lafrenière, McNicholas, Striker, and Welch 2024). We then completely describe the orbits of interval-closed set rowmotion on products of two chains $[2]\times[n]$ and use this understanding to prove a homomesy conjecture from (ELMSW 2024) involving the signed cardinality statistic. |
| title | Interval-closed set rowmotion and homomesy on products of two chains |
| topic | Combinatorics 05E15, 06A07 |
| url | https://arxiv.org/abs/2505.04000 |