42 citations · 73 across the 17 of their papers we have counts for
15 papers · 1 filter
Lineup polytopes of product of simplices
Federico Castillo, Jean-Philippe Labbé
Consider a real point configuration of size and an integer . The vertices of the -lineup polytope of correspond to the possible orderings…
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…
A pithy look at the Polytope Algebra
Federico Castillo
This is a hands on introduction to McMullen's Polytope Algebra. More than interesting on its own, this algebra was McMullen's tool to give a combinatorial proof of the g-theorem.
The permuto-associahedron revisited
Federico Castillo, Fu Liu
A classic problem connecting algebraic and geometric combinatorics is the realization problem: given a poset, determine whether there exists a polytope whose face lattice is the po…
Hopf monoids of ordered simplicial complexes
Federico Castillo, Jeremy L. Martin, Jose A. Samper
We study pure ordered simplicial complexes (i.e., simplicial complexes with a linear order on their ground sets) from the Hopf-theoretic point of view. We define a \textit{Hopf cla…
Minkowski summands of cubes
Federico Castillo, Joseph Doolittle, Bennet Goeckner +2
In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit comput…
Hopf monoids of ordered simplicial complexes
Federico Castillo, Jeremy Martin, Jose Alejandro Samper
We study ordered matroids and generalized permutohedra from a Hopf theoretic point of view. Our main object is a Hopf monoid in the vector species of extended generalized permutahe…
On the Todd Class of the Permutohedral variety
Federico Castillo, Fu Liu
In the special case of braid fans, we give a combinatorial formula for the Berline-Vergne's construction for an Euler-Maclaurin type formula that computes number of lattice points…
Coxeter submodular functions and deformations of Coxeter permutahedra
Federico Ardila, Federico Castillo, Christopher Eur +1
We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This family of polytopes contai…
Finiteness theorems for matroid complexes with prescribed topology
Federico Castillo, Jose Alejandro Samper
It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of -vectors, there are finitely ma…
Deformation Cones of nested Braid fans
Federico Castillo, Fu Liu
Generalized permutohedra are deformations of regular permutohedra, and arise in many different fields of mathematics. One important characterization of generalized permutohedra is…
Smooth polytopes with negative Ehrhart coefficients
Federico Castillo, Fu Liu, Benjamin Nill +1
We present examples of smooth lattice polytopes in dimensions 3 and higher where each coefficient of their Ehrhart polynomials that can potentially be negative is indeed negative.…
Berline-Vergne valuation and generalized permutohedra
Federico Castillo, Fu Liu
Generalizing a conjecture by De Loera et al., we conjecture that integral generalized permutohedra all have positive Ehrhart coefficients. Berline and Vergne construct a valuation…
The topology of the external activity complex of a matroid
Federico Ardila, Federico Castillo, Jose Alejandro Samper
We prove that the external activity complex of a matroid is shellable. In fact, we show that every linear extension of LasVergnas's external/internal order $<_{…
The arithmetic Tutte polynomials of the classical root systems
Federico Ardila, Federico Castillo, Michael Henley
Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement c…