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Mouvement du pendule

Fink — 1860

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Matroids over a ring

Alex FinkLuca Moci — 2016

Journal of the European Mathematical Society

We introduce the notion of a matroid M over a commutative ring R , assigning to every subset of the ground set an R -module according to some axioms. When R is a field, we recover matroids. When R = , and when R 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 R is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and...

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