Is such “characteristic function” studied in matroid theory?

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As a beginner it seems to me such a function $F$ on a matroid $M$ seems very natural i.e. $F(A)=0$ if $A$ is an independent set and $F(A)=1$ if $A$ is dependent. But I don't know whether people considered it or it is indeed trivial? Thanks.







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  • I don't know of any nice characterizations of matroids involving the characteristic functions of the dependent or independent sets. This function doesn't contain any more information than the collections of sets themselves, and the matroid axioms don't have any kind of nice expression in terms of function language.
    – Joshua Mundinger
    Aug 18 at 22:47














up vote
0
down vote

favorite












As a beginner it seems to me such a function $F$ on a matroid $M$ seems very natural i.e. $F(A)=0$ if $A$ is an independent set and $F(A)=1$ if $A$ is dependent. But I don't know whether people considered it or it is indeed trivial? Thanks.







share|cite|improve this question






















  • I don't know of any nice characterizations of matroids involving the characteristic functions of the dependent or independent sets. This function doesn't contain any more information than the collections of sets themselves, and the matroid axioms don't have any kind of nice expression in terms of function language.
    – Joshua Mundinger
    Aug 18 at 22:47












up vote
0
down vote

favorite









up vote
0
down vote

favorite











As a beginner it seems to me such a function $F$ on a matroid $M$ seems very natural i.e. $F(A)=0$ if $A$ is an independent set and $F(A)=1$ if $A$ is dependent. But I don't know whether people considered it or it is indeed trivial? Thanks.







share|cite|improve this question














As a beginner it seems to me such a function $F$ on a matroid $M$ seems very natural i.e. $F(A)=0$ if $A$ is an independent set and $F(A)=1$ if $A$ is dependent. But I don't know whether people considered it or it is indeed trivial? Thanks.









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edited Aug 18 at 4:57









apanpapan3

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asked Aug 18 at 3:56









Jack Lo

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  • I don't know of any nice characterizations of matroids involving the characteristic functions of the dependent or independent sets. This function doesn't contain any more information than the collections of sets themselves, and the matroid axioms don't have any kind of nice expression in terms of function language.
    – Joshua Mundinger
    Aug 18 at 22:47
















  • I don't know of any nice characterizations of matroids involving the characteristic functions of the dependent or independent sets. This function doesn't contain any more information than the collections of sets themselves, and the matroid axioms don't have any kind of nice expression in terms of function language.
    – Joshua Mundinger
    Aug 18 at 22:47















I don't know of any nice characterizations of matroids involving the characteristic functions of the dependent or independent sets. This function doesn't contain any more information than the collections of sets themselves, and the matroid axioms don't have any kind of nice expression in terms of function language.
– Joshua Mundinger
Aug 18 at 22:47




I don't know of any nice characterizations of matroids involving the characteristic functions of the dependent or independent sets. This function doesn't contain any more information than the collections of sets themselves, and the matroid axioms don't have any kind of nice expression in terms of function language.
– Joshua Mundinger
Aug 18 at 22:47















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