The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids Article Swipe

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Matthew Baker , Oliver Lorscheid , Zach Walsh , Tianyi Zhang ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2404.10656

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.

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Matroid Foundation (evidence) Mathematics Combinatorics Computer science Business Political science Law

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2404.10656
PDF: https://arxiv.org/pdf/2404.10656
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4394906526

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DOI: https://doi.org/10.48550/arxiv.2404.10656

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Title: The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-04-16

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Authors: Matthew Baker, Oliver Lorscheid, Zach Walsh, Tianyi Zhang

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Landing page: https://arxiv.org/abs/2404.10656

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PDF URL: https://arxiv.org/pdf/2404.10656

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Concepts: Matroid, Foundation (evidence), Mathematics, Combinatorics, Computer science, Business, Political science, Law

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