Supersolvability and Freeness for ψ-Graphical Arrangements
Name
454_2015_Article_9684.pdf
Size
365.31 KB
Format
Adobe PDF
Checksum (MD5)
9f5178f66b009b881c753c796e7fb490
Author(s)
Mu, Lili
Stanley, Richard P
Date Issued
April 2015
Journal
Discrete & Computational Geometry
Publisher
Springer US
Citation
Mu, Lili, and Richard P. Stanley. “Supersolvability and Freeness for ψ-Graphical Arrangements.” Discrete & Computational Geometry 53.4 (2015): 965–970.
Version
Author's final manuscript
Abstract
Let G be a simple graph on the vertex set {v[subscript 1],…,v[subscript n]} with edge set E. Let K be a field. The graphical arrangement A[subscript G] in K[superscript n] is the arrangement x[subscript i]−x[subscript j]=0,v[subscript i]v[subscript j] ∈ E. An arrangement A is supersolvable if the intersection lattice L(c(A)) of the cone c(A) contains a maximal chain of modular elements. The second author has shown that a graphical arrangement A[subscript G] is supersolvable if and only if G is a chordal graph. He later considered a generalization of graphical arrangements which are called ψ-graphical arrangements. He conjectured a characterization of the supersolvability and freeness (in the sense of Terao) of a ψ-graphical arrangement. We provide a proof of the first conjecture and state some conditions on free ψ-graphical arrangements.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00454-015-9684-z
