Inductively Factored Signed-graphic Arrangements of Hyperplanes
نویسندگان
چکیده
In 1994, Edelman and Reiner characterized free and supersolvable hyperplane arrangements in the restricted interval [An−1, Bn]. In this paper, we give a characterization of inductively factored arrangements in this interval, and show that the same characterization also describes factored arrangements in this interval. These results use the compact notation of signed graphs introduced by Zaslavsky.
منابع مشابه
Nice Reflection Arrangements
The aim of this note is a classification of all nice and all inductively factored reflection arrangements. It turns out that apart from the supersolvable instances only the monomial groups G(r, r, 3) for r > 3 give rise to nice reflection arrangements. As a consequence of this and of the classification of all inductively free reflection arrangements from Hoge and Röhrle (2015) we deduce that th...
متن کاملNice Restrictions of Reflection Arrangements
In [5], Hoge and the second author classified all nice and all inductively factored reflection arrangements. In this note we extend this classification by determining all nice and all inductively factored restrictions of reflection arrangements.
متن کاملDivision of characteristic polynomials and the division theorem for free arrangements of hyperplanes
We consider the triple (A,A′,AH) of hyperplane arrangements and the division of their characteristic polynomials. We show that the freeness of A and the division of χ(A; t) by χ(A ; t) confirm the freeness ofA. The key ingredient of this “division theorem” on freeness is the fact that, if χ(A ; t) divides χ(A; t), then the same holds for the localization at the codimension three flat in H. This...
متن کاملSupersolvability of complementary signed-graphic hyperplane arrangements
We study a class of hyperplane arrangements associated to complementary signed graphs in which the positive part and the negative part are complementary to each other in Kn, the complete graph on n vertices. These arrangements form a subclass of the Dn arrangement but do not contain the An−1 arrangement. The main result says that the arrangement A(G) of a complementary signed graph G is superso...
متن کاملAn Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations
In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs, and show a characterization of those graphs. Moreover, we also describe a relation between signed graphs and a certain class of multiarrangeme...
متن کامل