4 papers · 1 filter
Computing parametric weighted Ehrhart polynomials of smooth polytopes
Daniel Hwang, Juliet Whidden, Josephine Yu
We show that when integral polytopes are deformed while keeping the same facet normal vectors, the coefficients of weighted Ehrhart and -polynomials are piecewise polynomial f…
Ehrhart Theory over Abelian Group Rings
Robert Davis, Jesús A. De Loera, Alexey Garber +3
We introduce a unified framework for Ehrhart theory in which lattice point enumerators take coefficients in an Abelian group ring, encoding substantially richer algebraic data than…
Tropicalizing Principal Minors of Positive Definite Matrices
Abeer Al Ahmadieh, Felipe Rincón, Cynthia Vinzant +1
We study the tropicalization of the image of the cone of positive definite matrices under the principal minors map. It is a polyhedral subset of the set of -concave functions on…
The Tropical Variety of Symmetric Rank 2 Matrices
May Cai, Kisun Lee, Josephine Yu
We study the tropicalization of the variety of symmetric rank two matrices. Analogously to the result of Markwig and Yu for general tropical rank two matrices, we show that it has…