The Gonality of Queen's Graphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913436049342464 |
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| author | Morrison, Ralph Speeter, Noah |
| author_facet | Morrison, Ralph Speeter, Noah |
| contents | In this paper we study queen's graphs, which encode the moves by a queen on an $n\times m$ chess board, through the lens of chip-firing games. We prove that their gonality is equal to $nm$ minus the independence number of the graph, and give a one-to-one correspondence between maximum independent sets and classes of positive rank divisors achieving gonality. We also prove an identical result for toroidal queen's graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04686 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Gonality of Queen's Graphs Morrison, Ralph Speeter, Noah Combinatorics Algebraic Geometry 14T99, 05C57, 05C69 In this paper we study queen's graphs, which encode the moves by a queen on an $n\times m$ chess board, through the lens of chip-firing games. We prove that their gonality is equal to $nm$ minus the independence number of the graph, and give a one-to-one correspondence between maximum independent sets and classes of positive rank divisors achieving gonality. We also prove an identical result for toroidal queen's graphs. |
| title | The Gonality of Queen's Graphs |
| topic | Combinatorics Algebraic Geometry 14T99, 05C57, 05C69 |
| url | https://arxiv.org/abs/2312.04686 |