7 citations · 11 across the 7 of their papers we have counts for
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A genetic algorithm to search the space of Ehrhart -vectors
Gabriele Balletti
We describe a genetic algorithm to find candidates for -vectors satisfying given properties in the space of integers vectors of finite length. We use an implementation of such…
Families of lattice polytopes of mixed degree one
Gabriele Balletti, Christopher Borger
It has been shown by Soprunov that the normalized mixed volume (minus one) of an -tuple of -dimensional lattice polytopes is a lower bound for the number of interior lattice…
Enumeration of lattice polytopes by their volume
Gabriele Balletti
A well known result by Lagarias and Ziegler states that there are finitely many equivalence classes of d-dimensional lattice polytopes having volume at most K, for fixed constants…
Laplacian Simplices Associated to Digraphs
Gabriele Balletti, Takayuki Hibi, Marie Meyer +1
We associate to a finite digraph a lattice polytope whose vertices are the rows of the Laplacian matrix of . This generalizes a construction introduced by Braun and th…
Universal inequalities in Ehrhart Theory
Gabriele Balletti, Akihiro Higashitani
In this paper, we show the existence of universal inequalities for the -vector of a lattice polytope P, that is, we show that there are relations among the coefficients of the…
Three-dimensional lattice polytopes with two interior lattice points
Gabriele Balletti, Alexander M. Kasprzyk
We classify the three-dimensional lattice polytopes with two interior lattice points. Up to unimodular equivalence there are 22,673,449 such polytopes. This classification allows u…
On the maximum dual volume of a canonical Fano polytope
Gabriele Balletti, Alexander M. Kasprzyk, Benjamin Nill
We give an upper bound on the volume vol(P*) of a polytope P* dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d. This bound, e…
Connectivity through bounds for the Castelnuovo-Mumford regularity
Gabriele Balletti
We present a simple method to obtain information regarding the connectivity of the 1-skeleta of a wide family of simplicial complexes through bounds for the Castelnuovo-Mumford reg…