Orbitmesy and promotion on self-dual posets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918131268583424 |
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| author | Banaian, Esther Barnard, Emily Chepuri, Sunita Striker, Jessica |
| author_facet | Banaian, Esther Barnard, Emily Chepuri, Sunita Striker, Jessica |
| contents | We introduce the notion of orbitmesy, which is related to homomesy, a central phenomenon in dynamical algebraic combinatorics. An orbit $O$ is said to be orbitmesic with respect to a statistic if the orbit's average statistic value is equal to the global average. We particularly focus on the action of promotion on increasing labelings of certain fence posets called zig-zag posets, and two statistics, the antipodal sum statistic and the total sum statistic. We classify all of the orbitmesic promotion orbits for the zig-zag poset with four elements. Along the way, we investigate how homomesy of one action can be used to find orbitmesic orbits for another action, for the same fixed statistic. We prove several general results which can be used to find infinite families of orbitmesic orbits for any self-dual poset. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbitmesy and promotion on self-dual posets Banaian, Esther Barnard, Emily Chepuri, Sunita Striker, Jessica Combinatorics 05E18, 06A07 We introduce the notion of orbitmesy, which is related to homomesy, a central phenomenon in dynamical algebraic combinatorics. An orbit $O$ is said to be orbitmesic with respect to a statistic if the orbit's average statistic value is equal to the global average. We particularly focus on the action of promotion on increasing labelings of certain fence posets called zig-zag posets, and two statistics, the antipodal sum statistic and the total sum statistic. We classify all of the orbitmesic promotion orbits for the zig-zag poset with four elements. Along the way, we investigate how homomesy of one action can be used to find orbitmesic orbits for another action, for the same fixed statistic. We prove several general results which can be used to find infinite families of orbitmesic orbits for any self-dual poset. |
| title | Orbitmesy and promotion on self-dual posets |
| topic | Combinatorics 05E18, 06A07 |
| url | https://arxiv.org/abs/2508.19440 |