Tutte polynomials in superspace

2024/04/01 by Brendon Rhoades, Vasu Tewari, Rhoades, Brendon +2 · 2 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2404.01450

openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We associate a quotient of superspace to any hyperplane arrangement by considering the differential closure of an ideal generated by powers of certain homogeneous linear forms. This quotient is a superspace analogue of the external zonotopal algebra, and it further contains the central zonotopal algebra in the appropriate grading. We show that an evaluation of the bivariate Tutte polynomial is the bigraded Hilbert series of this quotient. We then use this fact to construct an explicit basis for the Macaulay inverse. These results generalize those of Ardila-Postnikov and Holtz-Ron. We also discuss enumerative consequences of our results in the setting of hyperplane arrangements.

Cited by

• The superspace coinvariant ring of type B
• A proof of the Fields Conjectures

Related

• A Tutte polynomial for toric arrangements
• The Tutte Polynomial of Symmetric Hyperplane Arrangements
• Tutte Polynomials of Symmetric Hyperplane Arrangements
• Tutte polynomials of hyperplane arrangements and the finite field method
• Tutte Polynomial of Ideal Arrangement