Geodesic
Freeness of hyperplane arrangements between Boolean arrangements and Weyl arrangements of type \(B_{\ell}\)
Michele Torielli1 ; Shuhei Tsujie2
1Hokkaido University
2Hiroshima Kokusai Gakuin University
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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Every subarrangement of Weyl arrangements of type $ B_{\ell} $ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $ A_{\ell-1} $ and type $ B_{\ell} $ in terms of graphs. Recently, Suyama and the authors characterized freeness for subarrangements containing Boolean arrangements satisfying a certain condition. This article is a sequel to the previous work. Namely, we give a complete characterization for freeness of arrangements between Boolean arrangements and Weyl arrangements of type $ B_{\ell} $ in terms of graphs.
DOI : 10.37236/9341
Classification : 52C35, 32S22, 05C22, 20F55, 13N15
Mots-clés : hyperplane arrangements, Weyl arrangements, signed graphs, freeness

Michele Torielli  1   ; Shuhei Tsujie  2

1 Hokkaido University
2 Hiroshima Kokusai Gakuin University 
@article{10_37236_9341,
     author = {Michele Torielli and Shuhei Tsujie},
     title = {Freeness of hyperplane arrangements between {Boolean} arrangements and {Weyl} arrangements of type {\(B_{\ell}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {3},
     doi = {10.37236/9341},
     zbl = {1444.52011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9341/}
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Michele Torielli; Shuhei Tsujie. Freeness of hyperplane arrangements between Boolean arrangements and Weyl arrangements of type \(B_{\ell}\). The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9341

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