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Chain algebras of finite distributive lattices
We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes, we conclude that every such algebra is normal and Cohen–Macaulay, and give an interpretation of its Krull dimension in terms of the combinatorics of the under...
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| Published in: | Journal of algebraic combinatorics 2024, Vol.59 (2), p.473-494 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c351t-247fadc02c413c4cf8a8593d4052ed05fab706eccf23a35e028e6ffa38484d9b3 |
| container_end_page | 494 |
| container_issue | 2 |
| container_start_page | 473 |
| container_title | Journal of algebraic combinatorics |
| container_volume | 59 |
| creator | Gasanova, Oleksandra Nicklasson, Lisa |
| description | We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes, we conclude that every such algebra is normal and Cohen–Macaulay, and give an interpretation of its Krull dimension in terms of the combinatorics of the underlying lattice. When the lattice is planar, we show that the corresponding chain algebra is generated by a sortable set of monomials and is isomorphic to a Hibi ring of another finite distributive lattice. As a consequence, it has a defining toric ideal with a quadratic Gröbner basis, and its
h
-vector counts ascents in certain standard Young tableaux. If instead the lattice has dimension
n
>
2
, we show that the defining ideal has minimal generators of degree at least
n
. |
| doi_str_mv | 10.1007/s10801-023-01294-8 |
| format | article |
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h
-vector counts ascents in certain standard Young tableaux. If instead the lattice has dimension
n
>
2
, we show that the defining ideal has minimal generators of degree at least
n
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h
-vector counts ascents in certain standard Young tableaux. If instead the lattice has dimension
n
>
2
, we show that the defining ideal has minimal generators of degree at least
n
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h
-vector counts ascents in certain standard Young tableaux. If instead the lattice has dimension
n
>
2
, we show that the defining ideal has minimal generators of degree at least
n
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| fulltext | fulltext |
| identifier | ISSN: 0925-9899 |
| ispartof | Journal of algebraic combinatorics, 2024, Vol.59 (2), p.473-494 |
| issn | 0925-9899 1572-9192 1572-9192 |
| language | eng |
| recordid | cdi_swepub_primary_oai_DiVA_org_mdh_66082 |
| source | Springer Nature |
| subjects | Algebra Combinatorial analysis Combinatorics Computer Science Convex and Discrete Geometry Group Theory and Generalizations Hilbert series Koszul algebra Lattices Lattices (mathematics) Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Polytopes Toric ideal |
| title | Chain algebras of finite distributive lattices |
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