2 citations · 2 across the 3 of their papers we have counts for
6 papers
Prime Ideals and Projective Closure in the Boolean Polynomial Semiring
Tristan Bishop, Chris Eppolito, Radford Green +3
In this paper, we investigate two related questions concerning the Boolean polynomial semiring in two variables. First, we study prime ideals in , beginning with a…
Pythagorean Hyperplane Arrangements: Combinatorics of Gain Genericity
Chris Eppolito
We study Pythagorean hyperplane arrangements, originally defined by Zaslavsky. In this first part of a series on such arrangements, we introduce a new notion of genericity for such…
On Infinite Matroids with Strong Maps: Proto-exactness and Finiteness Conditions
Chris Eppolito, Jaiung Jun
This paper investigates infinite matroids from a categorical perspective. We prove that the category of infinite matroids is a proto-exact category in the sense of Dyckerhoff and K…
Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions
Eric Bucher, Chris Eppolito, Jaiung Jun +1
In this paper, we give a cancellation-free antipode formula for the matroid-minor Hopf algebra. We then explore applications of this formula. For example, the cancellation-free for…
Proto-exact categories of matroids, Hall algebras, and K-theory
Christopher Eppolito, Jaiung Jun, Matt Szczesny
This paper examines the category of pointed matroids and strong maps from the point of view of Hall algebras. We show that has the…
Hopf algebras for matroids over hyperfields
Christopher Eppolito, Jaiung Jun, Matt Szczesny
Recently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying theory of various generalizations of matroids. In this paper we generalize the not…