Mathematical morphology and poset geometry.
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Displaying 1 – 4 of 4
Matroid polytopes, nested sets and Bergman fans.
Feichtner, Eva Maria, Sturmfels, Bernd (2005)
Portugaliae Mathematica. Nova Série
Matroids over a ring
Alex Fink, Luca Moci (2016)
Journal of the European Mathematical Society
We introduce the notion of a matroid over a commutative ring , assigning to every subset of the ground set an -module according to some axioms. When is a field, we recover matroids. When , and when is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively. More generally, whenever is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and...
Minimality of toric arrangements
Giacomo d'Antonio, Emanuele Delucchi (2015)
Journal of the European Mathematical Society
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Currently displaying 1 – 4 of 4
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