6 papers
Positivity and log concavity of the Links--Gould polynomial of knots
Stavros Garoufalidis, Shana Yunsheng Li, Josephine Yu
Motivated by the recent work of Harper--Kohli--Song--Tahar, we formulate a positivity, hole-free, and log-concavity conjecture for the Links--Gould polynomial of alternating links…
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…
Real and Positive Tropicalizations of Symmetric Determinantal Varieties
Abeer Al Ahmadieh, May Cai, Josephine Yu
We study real and positive tropicalizations of the varieties of low rank symmetric matrices over real or complex Puiseux series. We show that real tropicalization coincides with co…
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…