Séminaire Lotharingien de Combinatoire, 93B.9 (2025), 12 pp.
Brendon Rhoades, Vasu Tewari and Andy Wilson
Tutte Polynomials in Superspace
Abstract.
We associate a quotient of superspace to any hyperplane arrangement by considering the differential closure of a ``power ideal'' (a particular ideal generated by powers of certain homogeneous linear forms).
This quotient is a superspace analogue of the external zonotopal algebra of Holtz and Ron and also contains the central zonotopal algebra. We show that the bigraded Hilbert series of this quotient is equal to an evaluation of the Tutte polynomial. We also construct an explicit basis for the Macaulay inverse.
These results generalize previous work of Ardila-Postnikov and Holtz-Ron.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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