Characteristic numbers and chromatic polynomial of a tensor

TL;DR

This paper introduces characteristic numbers and a chromatic polynomial for tensors, unifying various concepts across graph theory, algebraic geometry, and algebraic statistics.

Contribution

It generalizes and unifies the chromatic polynomial and characteristic numbers across multiple mathematical and statistical frameworks.

Findings

Defines characteristic numbers and chromatic polynomial for tensors

Unifies concepts from graph theory, algebraic geometry, and statistics

Provides a new framework for tensor invariants

Abstract

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.