The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids
Combinatorics
2025-05-16 v2
Abstract
We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we show that the foundation of a 2-sum of matroids is the absolute tensor product of the foundations, and that the foundation of a matroid is invariant under segment-cosegment exchange.
Cite
@article{arxiv.2404.10656,
title = {The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids},
author = {Matthew Baker and Oliver Lorscheid and Zach Walsh and Tianyi Zhang},
journal= {arXiv preprint arXiv:2404.10656},
year = {2025}
}
Comments
35 pages. v2: Added more background information and made minor expository changes