Author:
Defant Colin,Williams Nathan
Abstract
AbstractWe introducesemidistrim 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 theGalois 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.Semidistrim lattices have a naturalrowmotionoperator, which simultaneously generalizes Barnard’s$\overline \kappa $map on semidistributive lattices as well as Thomas and the second author’s rowmotion on trim lattices. Every lattice has an associatedpop-stack sortingoperator that sends an elementxto the meet of the elements covered byx. 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.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference50 articles.
1. Sortable elements and Cambrian lattices
2. [11] Choi, Y. and Sun, N. , ‘The image of the Pop operator on various lattices’, Preprint, 2022, arXiv:2209.13695.
3. Coxeter-biCatalan combinatorics
4. Free Lattices
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