Log-concavity and log-convexity via distributive lattices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910557490118656 |
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| author | Liang, Jinting Sagan, Bruce E. |
| author_facet | Liang, Jinting Sagan, Bruce E. |
| contents | We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal Lemma to prove log-concavity and log-convexity of various sequences involving lattice paths (Catalan, Motzkin and large Schröder numbers), intervals in Young's lattice, order polynomials, specializations of Schur and Schur Q-functions, Lucas sequences, descent and peak polynomials of permutations, pattern avoidance, set partitions, and noncrossing partitions. We end with a section with conjectures and outlining future directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log-concavity and log-convexity via distributive lattices Liang, Jinting Sagan, Bruce E. Combinatorics 05A20 (Primary) 05A05, 05A10, 05A18, 06D99 (Secondary) We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal Lemma to prove log-concavity and log-convexity of various sequences involving lattice paths (Catalan, Motzkin and large Schröder numbers), intervals in Young's lattice, order polynomials, specializations of Schur and Schur Q-functions, Lucas sequences, descent and peak polynomials of permutations, pattern avoidance, set partitions, and noncrossing partitions. We end with a section with conjectures and outlining future directions. |
| title | Log-concavity and log-convexity via distributive lattices |
| topic | Combinatorics 05A20 (Primary) 05A05, 05A10, 05A18, 06D99 (Secondary) |
| url | https://arxiv.org/abs/2408.02782 |