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Free Subarrangements of Shi Arrangements

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Abstract

Athanasiadis characterized the freeness of the cones of the arrangements between braid arrangements and Shi arrangements. We are interested in the subarrangements Shi(G) of Shi arrangements associated with a graph G, which may not contain all hyperplanes of braid arrangements. We classify the cones of the arrangements Shi(G) which are free. In the meanwhile, we give the graphical interpretation of the exponents of free arrangements \(\mathbf{c }\)(Shi(G)).

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References

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Acknowledgements

The authors thank Kyoji Saito for some nice discussions and the referees for comments and suggestions.

Funding

Supported by NSFC No.11071010.

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Authors and Affiliations

  1. College of mathematics and physics, Beijing University of Chemical Technology, Beijing, 100029, China

    Zixuan Wang & Guangfeng Jiang

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  1. Zixuan Wang
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  2. Guangfeng Jiang
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Correspondence to Guangfeng Jiang.

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Wang, Z., Jiang, G. Free Subarrangements of Shi Arrangements. Graphs and Combinatorics 38, 59 (2022). https://doi.org/10.1007/s00373-021-02399-2

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  • DOI: https://doi.org/10.1007/s00373-021-02399-2

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