Results 101 to 110 of about 20,001 (120)
Type 2 diabetes mellitus impairs tooth supraeruption by disrupting periapical alveolar bone remodeling. [PDF]
BMC Oral HealthShi J +7 more
europepmc +1 more source
Freeness for Restriction Arrangements of the Extended Shi and Catalan Arrangements
Discrete Mathematics, 2023 The extended Shi and Catalan arrangements are well investigated arrangements. In this paper, we prove that the cone of the extended Catalan arrangement of type A is always hereditarily free, while we determine the dimension in which the cone of the extended Shi arrangement of type A is hereditarily free.
Shuhei Tsujie, Norihiro Nakashima
exaly +4 more sources
On the Falk Invariant of Shi and Linial Arrangements [PDF]
Discrete and Computational Geometry, 2021 It is an open question to give a combinatorial interpretation of the Falk invariant of a hyperplane arrangement, i.e. the third rank of successive quotients in the lower central series of the fundamental group of the arrangement. In this article, we give a combinatorial formula for this invariant in the case of hyperplane arrangements that are complete
Michele Torielli, Weili Guo
exaly +5 more sources
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Free Subarrangements of Shi Arrangements
Graphs and Combinatorics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zixuan Wang, Guangfeng Jiang
exaly +3 more sources
Shi Threshold Arrangement [PDF]
Electronic Journal of Combinatorics, 2012 Richard Stanley suggested the problem of finding the number of regions and the characteristic polynomial of a certain hyperplane arrangement defined by $x_i + x_j=0,1$, which is called the Shi threshold arrangement. We present the answer of the problem, using the finite field method.
Seunghyun Seo
exaly +4 more sources
Ad-Nilpotent Ideals and the Shi Arrangement
Journal of Combinatorial Theory - Series A, 2013 We extend the Shi bijection from the Borel subalgebra case to parabolic subalgebras. In the process, the $I$-deleted Shi arrangement $\texttt{Shi}(I)$ naturally emerges. This arrangement interpolates between the Coxeter arrangement $\texttt{Cox}$ and the Shi arrangement $\texttt{Shi}$, and breaks the symmetry of $\texttt{Shi}$ in a certain symmetrical ...
Chao-Ping Dong
exaly +3 more sources
A Simple Bijection for the Regions of the Shi Arrangement of Hyperplanes
Discrete Mathematics, 1999 The Shi arrangement ${\mathcal S}_n$ is the arrangement of affine hyperplanes in ${\mathbb R}^n$ of the form $x_i - x_j = 0$ or $1$, for $1 \leq i < j \leq n$. It dissects ${\mathbb R}^n$ into $(n+1)^{n-1}$ regions, as was first proved by Shi. We give a simple bijective proof of this result. Our bijection generalizes easily to any subarrangement of $
Christos A. Athanasiadis
exaly +4 more sources
Hyperplane Arrangements Between Shi and Ish [PDF]
Electronic Notes in Discrete Mathematics, 2018 Abstract We introduce a new family of hyperplane arrangements in dimension n ≥ 3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions — the connected components of the complement of the union of the hyperplanes — which can be bijectively labeled with the ...
Rui Duarte, Antonio Guedes de Oliveira
exaly +4 more sources
Lattice Point Counts for the Shi Arrangement and Other Affinographic Hyperplane Arrangements
Journal of Combinatorial Theory - Series A, 2007 13 ...
Thomas Zaslavsky, David Forge
exaly +3 more sources