Parking trees and the toric g-vector of nestohedra
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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_ | 1866918387569917952 |
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| author | Ehrenborg, Richard Hetyei, Gábor Readdy, Margaret |
| author_facet | Ehrenborg, Richard Hetyei, Gábor Readdy, Margaret |
| contents | We express the toric g-vector entries of any simple polytope as a nonnegative integer linear combination of its gamma-vector entries. We show that the toric g-vector of the associahedron is the ascent statistic of 123-avoiding parking functions. An analogous result holds for the cyclohedron and 123-avoiding functions. We prove that the toric g-vector of the permutahedron records the ascent statistics of parking trees representing 123-avoiding parking functions. We indicate how our approach extends to all chordal nestohedra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parking trees and the toric g-vector of nestohedra Ehrenborg, Richard Hetyei, Gábor Readdy, Margaret Combinatorics Primary 05E45, 52B05, 52B12, Secondary 05A05, 05A15, 52B15, 52B20 We express the toric g-vector entries of any simple polytope as a nonnegative integer linear combination of its gamma-vector entries. We show that the toric g-vector of the associahedron is the ascent statistic of 123-avoiding parking functions. An analogous result holds for the cyclohedron and 123-avoiding functions. We prove that the toric g-vector of the permutahedron records the ascent statistics of parking trees representing 123-avoiding parking functions. We indicate how our approach extends to all chordal nestohedra. |
| title | Parking trees and the toric g-vector of nestohedra |
| topic | Combinatorics Primary 05E45, 52B05, 52B12, Secondary 05A05, 05A15, 52B15, 52B20 |
| url | https://arxiv.org/abs/2511.04815 |