Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 41 min ago
PreprintarXiv licencearXiv

Boolean building set arrangements

  • Leonie Mühlherr
  • Sven Wiesner
Open at sourcePDFDOICite

Abstract

In this article, we generalize the notion of connected subgraph arrangements, established by Cuntz and Kühne by allowing edges of cardinality greater than two, with a focus on local properties. We show that the class of free connected hypersubgraph arrangements is larger than the class of free connected subgraph arrangements, but that there exists a necessary condition for freeness that refers back to the graphic case. Furthermore, we obtain a unique description of these arrangements by associating them with Boolean building sets. We study the nested complex of the building set in relation to the lattice of intersections, and characterize all simplicial arrangements within this new class.

Related

  1. Topological line arrangements with high multiplicities
    Paolo Aceto, Marco Golla
    HALPreprintLicence not statedGeometry & topologyHAL
  2. On the proof of multi-variable n/d-conjecture for hyperplane arrangements
    Rui Tan, Fanghan Xiang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. A generalized Saito criterion, from line arrangements to curves
    Anca Măcinic
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Scopes arrangements and product formulas
    Huang Lin, Tao Qin
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Suciu's Conjecture on hyperplane arrangements
    Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{muhlherr2026boolean,
  title = {{Boolean building set arrangements}},
  author = {Leonie Mühlherr and Sven Wiesner},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21874},
  eprint = {2609.21874},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21874},
}
RIS
TY  - UNPB
TI  - Boolean building set arrangements
AU  - Leonie Mühlherr
AU  - Sven Wiesner
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21874
UR  - https://arxiv.org/abs/2609.21874
AB  - In this article, we generalize the notion of connected subgraph arrangements, established by Cuntz and Kühne by allowing edges of cardinality greater than two, with a focus on local properties. We show that the class of free connected hypersubgraph arrangements is larger than the class of free connected subgraph arrangements, but that there exists a necessary condition for freeness that refers back to the graphic case. Furthermore, we obtain a unique description of these arrangements by associating them with Boolean building sets. We study the nested complex of the building set in relation to the lattice of intersections, and characterize all simplicial arrangements within this new class.
ER  -