JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (12): 66-70.doi: 10.6040/j.issn.1671-9352.0.2014.187

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The freeness of Shi-Catalan arrangements of type G2

GAO Rui-mei   

  1. Department of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China
  • Received:2014-04-28 Revised:2014-09-09 Online:2014-12-20 Published:2014-12-20

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Abstract: The Shi-Catalan arrangements of type G2 are multiarrangements in the 2-dimensional vector space, which are obtained by giving the same multiplicity to the hyperplanes in the same orbit in Weyl arrangements of type G2. Four concrete forms of Shi-Catalan arrangements of type G2 are given. By counting the intersections of hyperplanes in reflection planes, we prove the conclusion that the cones over the Shi-Catalan arrangements of type G2 are all free.

Key words: Weyl arrangement, freeness, Shi-Catalan arrangement

CLC Number: 

  • O189
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[1] GAO Rui-mei, CHU Ying. Freeness of arrangements between the Weyl arrangements of types An-1 and Bn [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 70-75.
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