5 papers
A construction of polyptych lattices via a pair of Gorenstein PL cones
Laura Escobar, Megumi Harada, Christopher Manon
The theory of polyptych lattices seeks to incorporate, into a single combinatorial framework, the piecewise-linear bijections (mutations) that appear in many theories that generali…
Algebra and geometry of ASM weak order
Laura Escobar, Patricia Klein, Anna Weigandt
Much of modern Schubert calculus is centered on Schubert varieties in the complete flag variety and on their classes in its integral cohomology ring. Under the Borel isomorphism, t…
Oriented Matroid Circuit Polytopes
Laura Escobar, Jodi McWhirter
Matroids give rise to several natural constructions of polytopes. Inspired by this, we examine polytopes that arise from the signed circuits of an oriented matroid. We give the dim…
Gorenstein-Fano polytopes and compactifications of rank 2 polyptych lattices
Adrian Cook, Laura Escobar, Megumi Harada +1
The theory of polyptych lattices was introduced by Escobar, Harada, and Manon, in an effort to simultaneously generalize combinatorial and geometric phenomena seen in toric, cluste…
Geometric families of degenerations from mutations of polytopes
Laura Escobar, Megumi Harada, Christopher Manon
We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We also define and study PL (polyptych-lattice) polyt…