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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 080, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.080
(Mi sigma1617)
 

This article is cited in 1 scientific paper (total in 1 paper)

Modular Construction of Free Hyperplane Arrangements

Shuhei Tsujie

Department of Education, Hokkaido University of Education, Hokkaido, Japan
Full-text PDF (456 kB) Citations (1)
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Abstract: In this article, we study freeness of hyperplane arrangements. One of the most investigated arrangement is a graphic arrangement. Stanley proved that a graphic arrangement is free if and only if the corresponding graph is chordal and Dirac showed that a graph is chordal if and only if the graph is obtained by “gluing” complete graphs. We will generalize Dirac's construction to simple matroids with modular joins introduced by Ziegler and show that every arrangement whose associated matroid is constructed in the manner mentioned above is divisionally free. Moreover, we apply the result to arrangements associated with gain graphs and arrangements over finite fields.
Keywords: hyperplane arrangement, free arrangement, matroid, modular join, chordality.
Received: January 29, 2020; in final form August 13, 2020; Published online August 22, 2020
Bibliographic databases:
Document Type: Article
Language: English
Citation: Shuhei Tsujie, “Modular Construction of Free Hyperplane Arrangements”, SIGMA, 16 (2020), 080, 19 pp.
Citation in format AMSBIB
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\paper Modular Construction of Free Hyperplane Arrangements
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\vol 16
\papernumber 080
\totalpages 19
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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    Abstract page:87
    Full-text PDF :29
    References:24
     
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