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Differential operators, anisotropy, and simplicial spheres
Kalle Karu, Matt Larson, Alan Stapledon
We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These ident…
Fine multidegrees, universal Grobner bases, and matrix Schubert varieties
Daoji Huang, Matt Larson
We give a criterion for a collection of polynomials to be a universal Gröbner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $…
Determinants of Hodge-Riemann forms
Matt Larson, Isabella Novik, Alan Stapledon
We calculate the determinant of the bilinear form in middle degree of the generic artinian reduction of the Stanley-Reisner ring of an odd-dimensional simplicial sphere. This prove…
Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes
Joshua Brakensiek, Manik Dhar, Jiyang Gao +2
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A specia…
Straightening laws for Chow rings of matroids
Matt Larson
We give elementary and non-inductive proofs of three fundamental theorems about Chow rings of matroids: the standard monomial basis, Poincare duality, and the dragon-Hall-Rado form…