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About: Ingleton's inequality     Goto   Sponge   NotDistinct   Permalink

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Type: yago:Abstraction100002137yago:Attribute100024264yago:Difference104748836yago:Inequality104752221yago:Quality104723816yago:WikicatInequalities New Facet based on Instances of this Class

In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let ρ be its rank function, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality ρ(X1)+ρ(X2)+ρ(X1∪X2∪X3)+ρ(X1∪X2∪X4)+ρ(X3∪X4) ≤ ρ(X1∪X2)+ρ(X1∪X3)+ρ(X1∪X4)+ρ(X2∪X3)+ρ(X2∪X4) is satisfied.