Interpreting the (signed) chromatic polynomial coefficients via hyperplane arrangements
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866917038189969408 |
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| author | Goregaokar, Neha |
| author_facet | Goregaokar, Neha |
| contents | A recent result of Lofano and Paolini expresses the characteristic polynomial of a real hyperplane arrangement in terms of a projection statistic on the regions of the arrangement. We use this result to give an alternative proof for Greene and Zaslavsky's interpretation for the coefficients of the chromatic polynomial of a graph and further generalize this interpretation to signed graphs. We also show that this projection statistic has a nice combinatorial interpretation in the case of the braid arrangement, which generalizes to graphical arrangements of natural unit interval graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpreting the (signed) chromatic polynomial coefficients via hyperplane arrangements Goregaokar, Neha Combinatorics A recent result of Lofano and Paolini expresses the characteristic polynomial of a real hyperplane arrangement in terms of a projection statistic on the regions of the arrangement. We use this result to give an alternative proof for Greene and Zaslavsky's interpretation for the coefficients of the chromatic polynomial of a graph and further generalize this interpretation to signed graphs. We also show that this projection statistic has a nice combinatorial interpretation in the case of the braid arrangement, which generalizes to graphical arrangements of natural unit interval graphs. |
| title | Interpreting the (signed) chromatic polynomial coefficients via hyperplane arrangements |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.00941 |