Details
Original language | English |
---|---|
Publication status | E-pub ahead of print - 12 Jul 2023 |
Externally published | Yes |
Abstract
Keywords
- math.CO, 52C35, 32S22, 20F55, 51F15
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
2023.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Projective dimension of weakly chordal graphic arrangements
AU - Abe, Takuro
AU - Kühne, Lukas
AU - Mücksch, Paul
AU - Mühlherr, Leonie
N1 - 20 pages, 2 figures
PY - 2023/7/12
Y1 - 2023/7/12
N2 - 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.
AB - 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.
KW - math.CO
KW - 52C35, 32S22, 20F55, 51F15
M3 - Preprint
BT - Projective dimension of weakly chordal graphic arrangements
ER -