Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915074944270336 |
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| author | Elizalde, Sergi Lafrenière, Nadia Lewis, Joel Brewster McNicholas, Erin Striker, Jessica Welch, Amanda |
| author_facet | Elizalde, Sergi Lafrenière, Nadia Lewis, Joel Brewster McNicholas, Erin Striker, Jessica Welch, Amanda |
| contents | We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets of truncated rectangle posets, including the type $A$ root poset, by constructing a bijection to certain quarter-plane walks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks Elizalde, Sergi Lafrenière, Nadia Lewis, Joel Brewster McNicholas, Erin Striker, Jessica Welch, Amanda Combinatorics 05A15, 06A07 We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets of truncated rectangle posets, including the type $A$ root poset, by constructing a bijection to certain quarter-plane walks. |
| title | Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks |
| topic | Combinatorics 05A15, 06A07 |
| url | https://arxiv.org/abs/2412.16368 |