8 papers
Sylvester simplices: Triangulations and Ehrhart-theoretic aspects
Jhon B. Caicedo, Federico Castillo, Martina Juhnke +1
The Sylvester simplex is a -dimensional lattice simplex with exactly interior lattice points. Sylvester simplices are conjectured to be the volume maximi…
Polytopal bases for barycentric subdivisions
Spencer Backman, Federico Castillo
Several important fans studied at the interface of combinatorics and algebraic geometry arise from barycentric subdivisions of other fans; the central example is the braid arrangem…
Almost factorial many facets for 0/1-polytopes
Federico Castillo, Luis Ferroni
A long-standing question posed by Fukuda (1995) and Ziegler (2000) inquires about the asymptotic behavior of , the maximum number of facets that an -dimensional -poly…
A differential characterization of volume polynomials of permutohedra
Tristram Bogart, Federico Castillo, Damián de la Fuente +1
We study a graded vector space of polynomials associated to a square matrix, defined by a finite difference condition along the rows. We show this space coincides with one defined…
Paper BOAT
Federico Castillo, Damian de la Fuente, Nicolas Libedinsky +1
We derive a formula for computing the size of lower Bruhat intervals for elements in the dominant cone of an affine Weyl group of type . This enumeration problem is reduced to c…
Solving one-body ensemble N-representability problems with spin
Julia Liebert, Federico Castillo, Jean-Philippe Labbé +2
The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies of orbitals according to $0 \leq…
Symmetrizing polytopes and posets
Federico Castillo, Fu Liu
Motivated by the authors' work on permuto-associahedra, which can be considered as a symmetrization of the associahedron using the symmetric group, we introduce and study the $\mat…
On the size of Bruhat intervals
Federico Castillo, Damian de la Fuente, Nicolas Libedinsky +1
For affine Weyl groups and elements associated to dominant coweights, we present a convex geometry formula for the size of the corresponding lower Bruhat intervals. Extensive compu…