منابع مشابه
Auspicious Tatami Mat Arrangements
The main purpose of this paper is to introduce the idea of tatami tilings, and to present some of the many interesting and fun questions that arise when studying them. Roughly speaking, we are considering are tilings of rectilinear regions with 1×2 dimer tiles and 1×1 monomer tiles, with the constraint that no four corners of the tiles meet. Typical problems are to minimize the number of monome...
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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...
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Let V be a finite dimensional complex vector space and W ⊂ GL(V ) be a finite complex reflection group. Let V reg be the complement in V of the reflecting hyperplanes. A classical conjecture predicts that V reg is a K(π, 1) space. When W is a complexified real reflection group, the conjecture follows from a theorem of Deligne, [20]. Our main result validates the conjecture for duality (or, equi...
متن کاملEigenspace Arrangements of Reflection Groups
The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W . In this paper we replace 1 with an arbitrary eigenvalue and study the topology and homology representation of the resulting poset. After posing the main question of whether this poset is shellable, we show that all its upper intervals are ...
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.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/8820