49 research outputs found
Threshold graphs, shifted complexes, and graphical complexes
We consider a variety of connections between threshold graphs, shifted
complexes, and simplicial complexes naturally formed from a graph. These
graphical complexes include the independent set, neighborhood, and dominance
complexes. We present a number of structural results and relations among them
including new characterizations of the class of threshold graphs.Comment: 9 pages, 2 figures; to appear in Discrete Mathematic
Projection volumes of hyperplane arrangements
We prove that for any finite real hyperplane arrangement the average
projection volumes of the maximal cones is given by the coefficients of the
characteristic polynomial of the arrangement. This settles the conjecture of
Drton and Klivans that this held for all finite real reflection arrangements.
The methods used are geometric and combinatorial. As a consequence we determine
that the angle sums of a zonotope are given by the characteristic polynomial of
the order dual of the intersection lattice of the arrangement