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.
The paper establishes equivalence between two prior definitions of weak order on ASM(n) and gives three explicit combinatorial descriptions of its covering relations plus a fiber characterization via bumpless pipe dreams.
citing papers explorer
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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.
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Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams
The paper establishes equivalence between two prior definitions of weak order on ASM(n) and gives three explicit combinatorial descriptions of its covering relations plus a fiber characterization via bumpless pipe dreams.