Base partition for mixed families of finitary and cofinitary matroids
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866916257987559424 |
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| author | Erde, Joshua Gollin, Pascal Joó, Attila Knappe, Paul Pitz, Max |
| author_facet | Erde, Joshua Gollin, Pascal Joó, Attila Knappe, Paul Pitz, Max |
| contents | Let ${\mathcal{M} = (M_i \colon i\in K)}$ be a finite or infinite family consisting of matroids on a common ground set $E$ each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each $M_i$, which covers the set $E$, and also a collection of bases which is pairwise disjoint, then there is a collection of bases which partitions $E$. We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_05601 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Base partition for mixed families of finitary and cofinitary matroids Erde, Joshua Gollin, Pascal Joó, Attila Knappe, Paul Pitz, Max Combinatorics Let ${\mathcal{M} = (M_i \colon i\in K)}$ be a finite or infinite family consisting of matroids on a common ground set $E$ each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each $M_i$, which covers the set $E$, and also a collection of bases which is pairwise disjoint, then there is a collection of bases which partitions $E$. We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC. |
| title | Base partition for mixed families of finitary and cofinitary matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1910.05601 |