Partially ordered sets of distributive type and algebras with straightening laws
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911449879674880 |
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| author | Hibi, Takayuki Fakhari, Seyed Amin Seyed |
| author_facet | Hibi, Takayuki Fakhari, Seyed Amin Seyed |
| contents | A finite poset (partially ordered set) $P$ with ${\hat 0}$ is called of distributive type if every interval $[{\hat 0}, a]$, $a \in P$, of $P$ is a distributive lattice. From a viewpoint of ASL's (algebras with straightening laws), the join-meet toric ring on a finite distributive lattice is generalized to an ASL on a finite poset of distributive type. Our target is the questions when a finite poset of distributive lattice is Cohen--Macaulay and when the ASL on it is Gorenstein. We focus on a natural class of finite posets of distributive type and study various aspects of the above questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partially ordered sets of distributive type and algebras with straightening laws Hibi, Takayuki Fakhari, Seyed Amin Seyed Commutative Algebra Combinatorics A finite poset (partially ordered set) $P$ with ${\hat 0}$ is called of distributive type if every interval $[{\hat 0}, a]$, $a \in P$, of $P$ is a distributive lattice. From a viewpoint of ASL's (algebras with straightening laws), the join-meet toric ring on a finite distributive lattice is generalized to an ASL on a finite poset of distributive type. Our target is the questions when a finite poset of distributive lattice is Cohen--Macaulay and when the ASL on it is Gorenstein. We focus on a natural class of finite posets of distributive type and study various aspects of the above questions. |
| title | Partially ordered sets of distributive type and algebras with straightening laws |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2602.14395 |