Covolume polynomials are characterized as the differential operators that preserve volume polynomials, and the resulting product theorem implies that intersections of algebraic matroids are algebraic.
Diagonalizations of denormalized volume polynomials
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abstract
We show that diagonalization, products and lower truncations preserve the property of being a denormalized volume polynomial. We also discuss an application to poset inequalities.
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Linear operators preserving volume polynomials
Covolume polynomials are characterized as the differential operators that preserve volume polynomials, and the resulting product theorem implies that intersections of algebraic matroids are algebraic.