Semidistrim Lattices
We introduce semidistrim lattices, a simultaneous generalization of semidistributive and trim lattices that preserves many of their common properties. We prove that the elements of a semidistrim lattice correspond to the independent sets in an associated graph called the Galois graph, that products...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000464/type/journal_article |
| _version_ | 1797802511711600640 |
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| author | Colin Defant Nathan Williams |
| author_facet | Colin Defant Nathan Williams |
| author_sort | Colin Defant |
| collection | DOAJ |
| description | We introduce semidistrim lattices, a simultaneous generalization of semidistributive and trim lattices that preserves many of their common properties. We prove that the elements of a semidistrim lattice correspond to the independent sets in an associated graph called the Galois graph, that products and intervals of semidistrim lattices are semidistrim and that the order complex of a semidistrim lattice is either contractible or homotopy equivalent to a sphere. |
| first_indexed | 2024-03-13T05:06:47Z |
| format | Article |
| id | doaj.art-614c4a96f9d642e482ca9e054fecf08f |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-13T05:06:47Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-614c4a96f9d642e482ca9e054fecf08f2023-06-16T08:51:42ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.46Semidistrim LatticesColin Defant0Nathan Williams1Massachusetts Institute of Technology; E-mail:University of Texas at Dallas; E-mail:We introduce semidistrim lattices, a simultaneous generalization of semidistributive and trim lattices that preserves many of their common properties. We prove that the elements of a semidistrim lattice correspond to the independent sets in an associated graph called the Galois graph, that products and intervals of semidistrim lattices are semidistrim and that the order complex of a semidistrim lattice is either contractible or homotopy equivalent to a sphere.https://www.cambridge.org/core/product/identifier/S2050509423000464/type/journal_article06B0506B1506D75 |
| spellingShingle | Colin Defant Nathan Williams Semidistrim Lattices Forum of Mathematics, Sigma 06B05 06B15 06D75 |
| title | Semidistrim Lattices |
| title_full | Semidistrim Lattices |
| title_fullStr | Semidistrim Lattices |
| title_full_unstemmed | Semidistrim Lattices |
| title_short | Semidistrim Lattices |
| title_sort | semidistrim lattices |
| topic | 06B05 06B15 06D75 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423000464/type/journal_article |
| work_keys_str_mv | AT colindefant semidistrimlattices AT nathanwilliams semidistrimlattices |