4 papers · 1 filter
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…