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The Ehrhart polynomial of a matroid specializes to the beta invariant
Anastasia Chavez, Galen Dorpalen-Barry, Luis Ferroni +3
We show that the linear coefficient of the Ehrhart polynomial of a matroid base polytope evaluated at is equal to, up to normalization, the -invariant of the matroid. This…
Partial permutohedra
Roger E. Behrend, Federico Castillo, Anastasia Chavez +4
Partial permutohedra are lattice polytopes which were recently introduced and studied by Heuer and Striker. For positive integers and , the partial permutohedron $\mathcal{P…
The lattice of cycles of an undirected graph
Gennadiy Averkov, Anastasia Chavez, Jesus A. De Loera +1
We study bases of the lattice generated by the cycles of an undirected graph, defined as the integer linear combinations of the 0/1-incidence vectors of cycles. We prove structural…
Catalan Recursion on Externally Ordered Bases of Unit Interval Positroids
Jan Tracy Camacho
The Catalan numbers form a sequence that counts over 200 combinatorial objects. A remarkable property of the Catalan numbers, which extends to these objects, is its recursive defin…
Quotients of uniform positroids
Carolina Benedetti, Anastasia Chavez, Daniel Tamayo
Flag matroids are a rich family of Coxeter matroids that can be characterized using pairs of matroids that form a quotient. We consider a class of matroids called positroids, intro…
Dyck Paths and Positroids from Unit Interval Orders
Anastasia Chavez, Felix Gotti
It is well known that the number of non-isomorphic unit interval orders on equals the -th Catalan number. Using work of Skandera and Reed and work of Postnikov, we show th…
The Dehn-Sommerville Relations and the Catalan Matroid
Anastasia Chavez, Nicole Yamzon
The -vector of a -dimensional polytope stores the number of faces of each dimension. When is simplicial the Dehn--Sommerville relations condense the -vector into t…