On z-Superstable and Critical Configurations of Chip Firing Pairs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916793080086528 |
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| author | Benton, Zach Kwak, Jane Oh, SuHo Torres, Mateo Xie, Mckinley |
| author_facet | Benton, Zach Kwak, Jane Oh, SuHo Torres, Mateo Xie, Mckinley |
| contents | It is well known that there is a duality map between the superstable configurations and the critical configurations of a graph. This was extended to all M-matrices in (Guzmàn-Klivans 2015). We show a natural way to extend this to all $(L,M)$-chip firing pairs introduced in (Guzmàn-Klivans 2016). In addition, we study various properties of this map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On z-Superstable and Critical Configurations of Chip Firing Pairs Benton, Zach Kwak, Jane Oh, SuHo Torres, Mateo Xie, Mckinley Combinatorics 05C50, 05C22, 20K01, 91A46 It is well known that there is a duality map between the superstable configurations and the critical configurations of a graph. This was extended to all M-matrices in (Guzmàn-Klivans 2015). We show a natural way to extend this to all $(L,M)$-chip firing pairs introduced in (Guzmàn-Klivans 2016). In addition, we study various properties of this map. |
| title | On z-Superstable and Critical Configurations of Chip Firing Pairs |
| topic | Combinatorics 05C50, 05C22, 20K01, 91A46 |
| url | https://arxiv.org/abs/2412.02679 |