From the 1 of 4 linked papers with an AI index.
4 papers
On the Log-submodularity for zonoids: from Mixed Volume inequalities to the Hypercube
Gennadiy Averkov, Katherina von Dichter, Ivan Soprunov
We prove a log-submodularity-type inequality for zonoids in , extending the three-dimensional result of Fradelizi, Madiman, Meyer, and Zvavitch. More generally, we co…
Mixed volumes of zonoids and the absolute value of the Grassmannian
Gennadiy Averkov, Katherina von Dichter, Simon Richard +1
The paper develops a combinatorial framework linking mixed volumes of zonoids with the absolute value image of the Grassmannian, and uses polyhedral computations to produce new Min…
On the discrete Heine-Shephard problem for four lattice polygons
Darren Gerrity, Ivan Soprunov
We study the set of square-free parts of volume polynomials associated with four planar lattice polytopes. This is motivated by the problem of describing possible pairwise intersec…
The volume polynomial of lattice polygons
Ivan Soprunov, Jenya Soprunova
We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the…