Echelonmotion, defined via the Bruhat decomposition of a poset's Cartan matrix, coincides with rowmotion on semidistributive lattices and on trim lattices under vertebral linear extensions, and echelon-independent lattices are exactly semidistributive.
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Rowmotion and Echelonmotion
Echelonmotion, defined via the Bruhat decomposition of a poset's Cartan matrix, coincides with rowmotion on semidistributive lattices and on trim lattices under vertebral linear extensions, and echelon-independent lattices are exactly semidistributive.