Quilts of Alternating Sign Matrices - From Boolean Lattices to Distributive Structures

Explore a mathematical lecture that delves into the fascinating world of quilts of alternating sign matrices and their relationship to posets. Learn how these mathematical objects generalize various concepts, including rank functions on submatrices, alternating sign matrices with corner sum matrices, and monotone Boolean functions. Discover how quilts form distributive lattices with unique properties and contain classical sublattices like matroids. Examine key enumerative results for specific cases involving antichains and chains, along with bounds for Boolean lattice scenarios. Understand the connections between quilts and Schubert varieties in both Grassmannian and complete flag manifolds, while exploring the computational complexity aspects related to Dedekind numbers. Engage with open problems and future research directions in this collaborative work presented by Sara Billey from the University of Washington, in partnership with Matjaž Konvalinka.