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- Title
Semidistrim Lattices.
- Authors
Defant, Colin; Williams, Nathan
- Abstract
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 semidistrimlattice correspond to the independent sets in an associated graph called the Galois graph, that products and intervals of semidistrimlattices are semidistrim and that the order complex of a semidistrim lattice is either contractible or homotopy equivalent to a sphere. Semidistrim lattices have a natural rowmotion operator, which simultaneously generalizes Barnard's - map on semidistributive lattices as well as Thomas and the second author's rowmotion on trim lattices. Every lattice has an associated pop-stack sorting operator that sends an element x to the meet of the elements covered by x. For semidistrim lattices, we are able to derive several intimate connections between rowmotion and pop-stack sorting, one of which involves independent dominating sets of the Galois graph.
- Subjects
INDEPENDENT sets; DOMINATING set; COMMONS; GENERALIZATION
- Publication
Forum of Mathematics, Sigma, 2023, Vol 11, p1
- ISSN
2050-5094
- Publication type
Article
- DOI
10.1017/fms.2023.46