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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…
An algebraic-combinatorial proof of a Bezout-type inequality for mixed volumes of three-dimensional zonoids
Gennadiy Averkov, Ivan Soprunov
We present a new algebraic-combinatorial approach to proving a Bezout-type inequality for zonoids in dimension three, which has recently been established by Fradelizi, Madiman, Mey…
On the affine permutation group of certain decreasing Cartesian codes
Eduardo Camps-Moreno, Hiram H. López, Eliseo Sarmiento +1
A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (s…