Supersolvability and Freeness for ψ-Graphical Arrangements
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/104653 https://orcid.org/0000-0003-3123-8241 |
| Summary: | 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. |
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