A family of rank $4$ non-algebraic matroids with pseudomodular dual
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915615674990592 |
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| author | Hochstättler, Winfried |
| author_facet | Hochstättler, Winfried |
| contents | The Tic-Tac-Toe matroid is a paving matroid of rank $5$ on 9
elements which is pseudomodular and whose dual is non-algebraic. It
has been proposed as a possible example of an algebraic matroid
whose dual is not algebraic. We present an infinite family of
matroids sharing these properties and generalizing the Tic-Tac-Toe matroid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A family of rank $4$ non-algebraic matroids with pseudomodular dual Hochstättler, Winfried Combinatorics 05B35, 12F20 The Tic-Tac-Toe matroid is a paving matroid of rank $5$ on 9 elements which is pseudomodular and whose dual is non-algebraic. It has been proposed as a possible example of an algebraic matroid whose dual is not algebraic. We present an infinite family of matroids sharing these properties and generalizing the Tic-Tac-Toe matroid. |
| title | A family of rank $4$ non-algebraic matroids with pseudomodular dual |
| topic | Combinatorics 05B35, 12F20 |
| url | https://arxiv.org/abs/2511.10417 |