Is such âcharacteristic functionâ 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.
characteristic-functions matroids
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up vote
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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.
characteristic-functions matroids
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.
â Joshua Mundinger
Aug 18 at 22:47
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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.
characteristic-functions matroids
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.
characteristic-functions matroids
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.
â Joshua Mundinger
Aug 18 at 22:47
add a comment |Â
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.
â 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.
â 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.
â Joshua Mundinger
Aug 18 at 22:47
add a comment |Â
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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.
â Joshua Mundinger
Aug 18 at 22:47