K-classes of delta-matroids and equivariant localization

TL;DR

This paper explores the geometric interpretation of the interlace polynomial of delta-matroids through K-theory, introducing a new formula for type B permutohedral varieties.

Contribution

It develops a new Hirzebruch-Riemann-Roch-type formula for type B permutohedral varieties and connects delta-matroid invariants with algebraic geometry.

Findings

Geometric interpretation of the interlace polynomial

New Riemann-Roch-type formula for type B permutohedral variety

Connection between delta-matroids and algebraic geometry

Abstract

Delta-matroids are "type B" generalizations of matroids in the same way that maximal orthogonal Grassmannians are generalizations of Grassmannians. A delta-matroid analogue of the Tutte polynomial of a matroid is the interlace polynomial. We give a geometric interpretation for the interlace polynomial via the K-theory of maximal orthogonal Grassmannians. To do so, we develop a new Hirzebruch-Riemann-Roch-type formula for the type B permutohedral variety.