Simplicial arrangements with special vertex

Michael Cuntz

Simplicial arrangements with special vertex

Michael Cuntz

Institute of Algebra, Number Theory and Discrete Mathematics

Research output: Working paper/Preprint › Preprint

Abstract

Shi-Catalan and affine Weyl arrangements are obtained in a similar way: they consist of a Weyl arrangement embedded into a higher dimensional space together with shifted copies. We consider the more general case when the Weyl arrangement is replaced by an arbitrary finite arrangement of hyperplanes. Such an arrangement is called an arrangement with special vertex. As our main result we prove that the number of parallel classes of lines in certain simplicial arrangements with special vertex is at most 12.

Original language	English
Number of pages	9
Publication status	E-pub ahead of print - 20 Jul 2026

Access to Document

https://arxiv.org/abs/2607.17785Licence: Arxiv nonexclusive-distrib 1.0

Cite this

@techreport{e3840dae67814f8a8fe238ea0d9ad042,

title = "Simplicial arrangements with special vertex",

abstract = "Shi-Catalan and affine Weyl arrangements are obtained in a similar way: they consist of a Weyl arrangement embedded into a higher dimensional space together with shifted copies. We consider the more general case when the Weyl arrangement is replaced by an arbitrary finite arrangement of hyperplanes. Such an arrangement is called an arrangement with special vertex. As our main result we prove that the number of parallel classes of lines in certain simplicial arrangements with special vertex is at most 12.",

author = "Michael Cuntz",

year = "2026",

month = jul,

day = "20",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Simplicial arrangements with special vertex

AU - Cuntz, Michael

PY - 2026/7/20

Y1 - 2026/7/20

N2 - Shi-Catalan and affine Weyl arrangements are obtained in a similar way: they consist of a Weyl arrangement embedded into a higher dimensional space together with shifted copies. We consider the more general case when the Weyl arrangement is replaced by an arbitrary finite arrangement of hyperplanes. Such an arrangement is called an arrangement with special vertex. As our main result we prove that the number of parallel classes of lines in certain simplicial arrangements with special vertex is at most 12.

AB - Shi-Catalan and affine Weyl arrangements are obtained in a similar way: they consist of a Weyl arrangement embedded into a higher dimensional space together with shifted copies. We consider the more general case when the Weyl arrangement is replaced by an arbitrary finite arrangement of hyperplanes. Such an arrangement is called an arrangement with special vertex. As our main result we prove that the number of parallel classes of lines in certain simplicial arrangements with special vertex is at most 12.

M3 - Preprint

BT - Simplicial arrangements with special vertex

ER -