A Consistent Sandpile Torsor Algorithm for Regular Matroids
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912513783758848 |
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| author | Ding, Changxin McDonough, Alex Tóthmérész, Lilla Yuen, Chi Ho |
| author_facet | Ding, Changxin McDonough, Alex Tóthmérész, Lilla Yuen, Chi Ho |
| contents | Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion of consistency to describe classes of actions that respect deletion-contraction in a precise sense, and proved the consistency of rotor-routing torsors (and uniqueness thereof) for plane graphs.
In this work, we prove that the class of actions introduced by Backman, Baker, and the fourth author, is consistent for regular matroids. More precisely, we prove the consistency of its generalization given by Backman, Santos and the fourth author, and independently by the first author. This extends the above existence assertion, as well as makes progress on the goal of classifying all consistent actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Consistent Sandpile Torsor Algorithm for Regular Matroids Ding, Changxin McDonough, Alex Tóthmérész, Lilla Yuen, Chi Ho Combinatorics 05B35, 05E18 Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion of consistency to describe classes of actions that respect deletion-contraction in a precise sense, and proved the consistency of rotor-routing torsors (and uniqueness thereof) for plane graphs. In this work, we prove that the class of actions introduced by Backman, Baker, and the fourth author, is consistent for regular matroids. More precisely, we prove the consistency of its generalization given by Backman, Santos and the fourth author, and independently by the first author. This extends the above existence assertion, as well as makes progress on the goal of classifying all consistent actions. |
| title | A Consistent Sandpile Torsor Algorithm for Regular Matroids |
| topic | Combinatorics 05B35, 05E18 |
| url | https://arxiv.org/abs/2407.03999 |