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Projective dimension of weakly chordal graphic arrangements

Research output: Working paper/PreprintPreprint

Authors

  • Takuro Abe
  • Lukas Kühne
  • Paul Mücksch
  • Leonie Mühlherr

External Research Organisations

  • Rikkyo University
  • Bielefeld University

Details

Original languageEnglish
Publication statusE-pub ahead of print - 12 Jul 2023
Externally publishedYes

Abstract

A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Reiner states that a graphic arrangement is free if and only if the corresponding graph is chordal, i.e., the graph has no chordless cycle with four or more vertices. In this article we extend this result by proving that the module of logarithmic derivations of a graphic arrangement has projective dimension at most one if and only if the corresponding graph is weakly chordal, i.e., the graph and its complement have no chordless cycle with five or more vertices.

Keywords

    math.CO, 52C35, 32S22, 20F55, 51F15

Cite this

Projective dimension of weakly chordal graphic arrangements. / Abe, Takuro; Kühne, Lukas; Mücksch, Paul et al.
2023.

Research output: Working paper/PreprintPreprint

Abe, T, Kühne, L, Mücksch, P & Mühlherr, L 2023 'Projective dimension of weakly chordal graphic arrangements'.
Abe, T., Kühne, L., Mücksch, P., & Mühlherr, L. (2023). Projective dimension of weakly chordal graphic arrangements. Advance online publication.
Abe T, Kühne L, Mücksch P, Mühlherr L. Projective dimension of weakly chordal graphic arrangements. 2023 Jul 12. Epub 2023 Jul 12.
Abe, Takuro ; Kühne, Lukas ; Mücksch, Paul et al. / Projective dimension of weakly chordal graphic arrangements. 2023.
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