A Note on Extension Properties and Representations of Matroids
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915163649605632 |
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| author | Bamiloshin, Michael Farràs, Oriol Padró, Carles |
| author_facet | Bamiloshin, Michael Farràs, Oriol Padró, Carles |
| contents | We discuss several extension properties of matroids and polymatroids and their application as necessary conditions for the existence of different matroid representations, namely linear, folded linear, algebraic, and entropic representations. Iterations of those extension properties are checked for matroids on eight and nine elements by means of computer-aided explorations, finding in that way several new examples of non-linearly representable matroids. A special emphasis is made on sparse paving matroids on nine points containing the tic-tac-toe configuration. We present a new, more clear description of that family and we analyze extension properties on those matroids and their duals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15085 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Note on Extension Properties and Representations of Matroids Bamiloshin, Michael Farràs, Oriol Padró, Carles Combinatorics 05B35, 94A15, 94A62 We discuss several extension properties of matroids and polymatroids and their application as necessary conditions for the existence of different matroid representations, namely linear, folded linear, algebraic, and entropic representations. Iterations of those extension properties are checked for matroids on eight and nine elements by means of computer-aided explorations, finding in that way several new examples of non-linearly representable matroids. A special emphasis is made on sparse paving matroids on nine points containing the tic-tac-toe configuration. We present a new, more clear description of that family and we analyze extension properties on those matroids and their duals. |
| title | A Note on Extension Properties and Representations of Matroids |
| topic | Combinatorics 05B35, 94A15, 94A62 |
| url | https://arxiv.org/abs/2306.15085 |