Freeness of hyperplane arrangements associated with gain graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910401354006528 |
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| author | Suyama, Daisuke Torielli, Michele Tsujie, Shuhei |
| author_facet | Suyama, Daisuke Torielli, Michele Tsujie, Shuhei |
| contents | Athanasiadis studied arrangements obtained by adding shifted hyperplanes to the braid arrangement. Similarly, Bailey studied arrangements obtained by adding tilted hyperplanes to the braid arrangement. These two kinds of arrangements are associated with directed graphs and their freeness was characterized in terms of the associated graphs. In addition, there is coincidence of freeness. Namely, if Athanasiadis' arrangement is free, then the corresponding Bailey's arrangement is free, and vice versa.
In this paper, we generalize this phenomenon by using gain graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Freeness of hyperplane arrangements associated with gain graphs Suyama, Daisuke Torielli, Michele Tsujie, Shuhei Combinatorics 52C35, 32S22, 05C22, 13N15 Athanasiadis studied arrangements obtained by adding shifted hyperplanes to the braid arrangement. Similarly, Bailey studied arrangements obtained by adding tilted hyperplanes to the braid arrangement. These two kinds of arrangements are associated with directed graphs and their freeness was characterized in terms of the associated graphs. In addition, there is coincidence of freeness. Namely, if Athanasiadis' arrangement is free, then the corresponding Bailey's arrangement is free, and vice versa. In this paper, we generalize this phenomenon by using gain graphs. |
| title | Freeness of hyperplane arrangements associated with gain graphs |
| topic | Combinatorics 52C35, 32S22, 05C22, 13N15 |
| url | https://arxiv.org/abs/2403.08304 |