Topics in Hyperplane Arrangements, Polytopes and Box-Splines

By C. Concini, C. Procesi. 2010

141 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Matroids over a ring (2012, background): “attice Zn by the sublattices spanned by subsets of vectors. From a list of vectors with integer coordinates one may produce objects like a toric arrangement, a partition function, and a zonotope (see [8]). In order to have a combinatorial structure from which these objects may be read oﬀ, one needs ”
Arithmetic matroids, the Tutte polynomial and toric arrangements (2011, background): “lications. In particular it encodes much combinatorial information on toric arrangements (as we will recall in Section 4), on zonotopes ([4]), and on Dahmen-Micchelli spaces ([22], [6], [5]; see also [9], [17], [19] for related topics). It has been shown in [22] that if MX is representable, the coeﬃ”
A Tutte polynomial for toric arrangements (2009, background): “ and Micchelli to study box splines and partition functions, and are deeply related respectively with the hyperplane arrangement and the toric arrangement dened by X, as explained in the recent book [9]. In particular, T X(1;y) is known to be the Hilbert series of D(X), and we will show that M X(1;y”