5 papers
Realizable Standard Young Tableaux
Igor Araujo, Alexander E. Black, Amanda Burcroff +3
Given two vectors and , their outer sum is given by the matrix with entries . If the entries of and are increasing and sufficiently gener…
Billey-Postnikov posets, rationally smooth Schubert varieties, and Poincaré duality
Christian Gaetz, Yibo Gao
Billey-Postnikov (BP) decompositions govern when Schubert varieties decompose as bundles of smaller Schubert varieties. We further develop the theory of BP decompositions an…
Coxeter Condorcet domains
Yibo Gao, Yulin Peng
Condorcet domains are subsets of permutations that ensure pairwise majority voting yields acyclic outcomes, and they form an active area of research at the intersection of social c…
MacNeille completions of parabolic quotients
Yibo Gao, Hanlin Xu
Alternating sign matrices (ASMs) arise as the Dedekind-MacNeille completion of the Bruhat order on the symmetric group. They enjoy fruitful combinatorial and geometric properties,…
Interlacing triangles, Schubert puzzles, and graph colorings
Christian Gaetz, Yibo Gao
We show that interlacing triangular arrays, introduced by Aggarwal-Borodin-Wheeler to study certain probability measures, can be used to compute structure constants for multiplying…