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.
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