5 papers
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…
Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras
Esther Banaian, Elise Catania, Christian Gaetz +3
We study a twisted version of Fraser, Lam, and Le's higher boundary measurement map, using face weights instead of edge weights, thereby providing Laurent polynomial expansions, in…
Poset topology, moves, and Bruhat interval polytope lattices
Christian Gaetz, Patricia Hersh
We study the poset topology of lattices arising from orientations of 1-skeleta of directionally simple polytopes, with Bruhat interval polytopes as our main example. We s…
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…
Canonical forms of polytopes from adjoints
Christian Gaetz
Projectivizations of pointed polyhedral cones are positive geometries in the sense of Arkani-Hamed, Bai, and Lam. Their canonical forms look like $$ Ω_C(x)=\frac{A(x)}{B(x)} d…