The freeness of Ish arrangements
نویسندگان
چکیده
منابع مشابه
Freeness and Multirestriction of Hyperplane Arrangements
Generalizing a result of Yoshinaga in dimension 3, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced characteristic polynomial equals the characteristic polynomial of this restriction. We show that the same statement holds true in any dimension when imposing certain tam...
متن کاملSupersolvability and Freeness for ψ-Graphical Arrangements
Let G be a simple graph on the vertex set {v1, . . . , vn} with edge set E. Let K be a field. The graphical arrangement AG in K n is the arrangement xi − xj = 0, vivj ∈ 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 AG is supersolvable if and only if ...
متن کاملThe freeness of ideal subarrangements of Weyl arrangements
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by ...
متن کاملExtensions of the Shi/ish Duality
We generalize a known bijection between the regions of the Shi and Ish hyperplane arrangements to a bijection between the regions of the nested-Ish and extendedShi arrangements. Although our bijection does not preserve the degrees of freedom statistic, we show that several of the steps do preserve this information, and we give formulas for the number of regions of each arrangement with a given ...
متن کاملA UK NEQAS ISH multicenter ring study using the Ventana HER2 dual-color ISH assay.
We performed a multicenter assessment of a new HER2 dual-color chromogenic in situ hybridization (CISH) test and herein report on concordance of CISH data with fluorescence in situ hybridization (FISH) data and intraobserver and interlaboratory scoring consistency. HER2 results were evaluated using duplicate cores from 30 breast cancers in 5 laboratories using the Ventana HER2 dual-color ISH as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2017
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.09.008