{"id":"hexagon/2610.00497","pdf":"https://hexagonmath.org/pdf/2610.00497v1","url":"https://hexagonmath.org/abs/2610.00497v1","tags":["msc:06B05","msc:06B25","bounded lattice","formal verification","interval","maximal sublattice","semidistributive lattice"],"score":0,"title":"Maximal sublattices of finite semidistributive lattices: the complement need not be an interval","domain":"math.RA","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math.RA","summary":"Adams, Freese, Nation and Schmid proved that the complement of a maximal sublattice of a finite bounded lattice is an interval, and asked whether the same holds for finite semidistributive lattices; Adaricheva, Mata, Silberger and Zamojska-Dzienio conjectured that it does. It does not. In a 26-element semidistributive sublattice of the square of a 14-element semidistributive lattice, the diagonal is a maximal sublattice whose complement has two minimal elements.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}