Matroid correspondence
Combinatorics
2026-07-15 v1 Commutative Algebra
Algebraic Geometry
Abstract
Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues. A matroid correspondence defines a functor between poset categories of matroids whose morphisms are matroid quotients, and various standard functors, including deletion, contraction, free extension, truncation, intersection, union, and pullback, arise in this way. We show that these correspondences preserve representability and algebraicity under natural hypotheses. In the polymatroid setting, we establish compatibility with multisymmetric lifts. Finally, we relate this construction to the supports of linear operators with Lorentzian symbols.
Cite
@article{arxiv.2607.13783,
title = {Matroid correspondence},
author = {Colin Crowley and Changxin Ding and Haoxi Hu and Arvind Kumar and Jonathan Montaño and Thai Thanh Nguyen and Anna Shapiro and Noah Solomon and Botong Wang and Juliet Whidden},
journal= {arXiv preprint arXiv:2607.13783},
year = {2026}
}