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- Ingleton's_inequality abstract "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 inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequalityρ(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.Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids. Although the article is mainly expository, in this paper Ingleton stated and proved Ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding.".
- Ingleton's_inequality wikiPageID "39661138".
- Ingleton's_inequality wikiPageRevisionID "597642741".
- Ingleton's_inequality id "p/t093890".
- Ingleton's_inequality title "Transmission rate of a channel".
- Ingleton's_inequality subject Category:Inequalities.
- Ingleton's_inequality subject Category:Matroid_theory.
- Ingleton's_inequality comment "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.".
- Ingleton's_inequality label "Ingleton's inequality".
- Ingleton's_inequality sameAs m.0w1dl3b.
- Ingleton's_inequality sameAs Q17086178.
- Ingleton's_inequality sameAs Q17086178.
- Ingleton's_inequality wasDerivedFrom Ingleton's_inequality?oldid=597642741.
- Ingleton's_inequality isPrimaryTopicOf Ingleton's_inequality.