Characteristic numbers and chromatic polynomial of a tensor

Austin Conner; Mateusz Micha{\l}ek

Characteristic numbers and chromatic polynomial of a tensor

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arxiv 2111.00809 v1 pith:Q4FMVQ3I submitted 2021-11-01 math.AG math.ACmath.CO

Austin Conner , Mateusz Micha{l}ek This is my paper · ORCID

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keywords characteristicnumberschromaticpolynomialcomplementstensoralgebraicapproach

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We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, characteristic numbers of quadrics in Schubert calculus, Betti numbers of complements of hyperplane arrangements and Euler characteristic of complements of determinantal hypersurfaces and the maximum likelihood degree for general linear concentration models in algebraic statistics.

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Mixed Eulerian numbers and beyond
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First explicit formula for mixed Eulerian numbers, and proof that matroidal mixed Eulerian numbers determine Derksen's G-invariant.

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