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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.02526 |
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| _version_ | 1866916644688756736 |
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| author | Brauner, Sarah Dorpalen-Barry, Galen Kara, Selvi Klivans, Caroline Schneider, Lisa |
| author_facet | Brauner, Sarah Dorpalen-Barry, Galen Kara, Selvi Klivans, Caroline Schneider, Lisa |
| contents | Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize chip-firing on graphs to higher dimensions, wherein graphs are replaced by cellular complexes and chip firing becomes flow-rerouting along the faces of the complex. Given such a system, it is natural to ask (1) whether this firing process terminates and (2) if it terminates uniquely (e.g. is confluent). In the graphical case, these questions were definitively answered by Bjorner--Lovasz--Shor, who developed three regimes which completely determine if a given system will terminate. Building on the work of Duval--Klivans--Martin and Felzenszwalb-Klivans, we answer these questions in a context called flow-firing, where the cellular complexes are 2-dimensional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02526 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Three-Regime Theorem for Flow-Firing Brauner, Sarah Dorpalen-Barry, Galen Kara, Selvi Klivans, Caroline Schneider, Lisa Combinatorics Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize chip-firing on graphs to higher dimensions, wherein graphs are replaced by cellular complexes and chip firing becomes flow-rerouting along the faces of the complex. Given such a system, it is natural to ask (1) whether this firing process terminates and (2) if it terminates uniquely (e.g. is confluent). In the graphical case, these questions were definitively answered by Bjorner--Lovasz--Shor, who developed three regimes which completely determine if a given system will terminate. Building on the work of Duval--Klivans--Martin and Felzenszwalb-Klivans, we answer these questions in a context called flow-firing, where the cellular complexes are 2-dimensional. |
| title | A Three-Regime Theorem for Flow-Firing |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2303.02526 |