Introduces 0-Hecke action to define weak order and descent sets on MacNeille completion of Bruhat order, proves vertex-decomposability of subword complex unions, proves Escobar-Klein-Weigandt conjecture on Cohen-Macaulay ASM varieties, gives counterexample to Hamaker-Reiner conjecture, and shows Mac
Algebra and geometry of ASM weak order.arXiv preprint arXiv:2502.19266
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The Dedekind-MacNeille completion of Bruhat orders on parabolic quotients of the symmetric group is a subposet of alternating sign matrices whose meet and join operations correspond to unions and intersections of ASM varieties.
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Weak Order on the MacNeille Completion of Bruhat Order
Introduces 0-Hecke action to define weak order and descent sets on MacNeille completion of Bruhat order, proves vertex-decomposability of subword complex unions, proves Escobar-Klein-Weigandt conjecture on Cohen-Macaulay ASM varieties, gives counterexample to Hamaker-Reiner conjecture, and shows Mac
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MacNeille completions of parabolic quotients
The Dedekind-MacNeille completion of Bruhat orders on parabolic quotients of the symmetric group is a subposet of alternating sign matrices whose meet and join operations correspond to unions and intersections of ASM varieties.