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The characteristic polynomial of the mixed arrangement

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Wuhan University Journal of Natural Sciences

Abstract

We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Möbius function of the mixed arrangement and the original hyperplane arangement. The Möbius function of the mixed arrangement is equal to the positive or the negative Möbius function of original hyperplane arrangement. Moreover, we give an equality of the chambers and the characteristic polynomial for the mixed arrangement.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China

    Su Dan & Zhang Dunmu

  2. School of Information Technology and Management Engineering, University of International Business and Economics, Beijing, 100029, China

    Su Dan

Authors
  1. Su Dan
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  2. Zhang Dunmu
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Correspondence to Zhang Dunmu.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China(10471020)

Biography: SU Dan(1977-), female, Ph.D. candidate, Lecturer of University of International Business and Economics, research direction: singularity theory and its applications.

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Su, D., Zhang, D. The characteristic polynomial of the mixed arrangement. Wuhan Univ. J. of Nat. Sci. 12, 203–206 (2007). https://doi.org/10.1007/s11859-006-0007-3

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  • DOI: https://doi.org/10.1007/s11859-006-0007-3

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