f-vector?

[Stefan van Zwam]

Hi all,

It seems that f-vector is a muddy concept. In Sage's matroid code, the f-vector is (a_0, ..., a_r) where a_i denotes the number of rank-i flats. In this paper by Lenz it is the vector (f_0, ..., f_r) where f_i is the number of independent sets of size i:

http://arxiv.org/pdf/1106.2944v4.pdf

and in this paper, it's a vector based on the order complex of the lattice of flats:

http://arxiv.org/pdf/math/0405535.pdf

So I guess that, unless there is some evidence that the Sage-usage appears in the literature as well, the name of that method should be changed.

--Stefan.

[Rudi Pendavingh]

Hi Stefan,

I think the term f-vector is defined for any graded lattice on a set X. The i-the entry of that f-vector counts the number of elements of X of rank i. 

What I called the f-vector of a matroid is the f-vector of its lattice of flats. I thought that was the usual meaning of the term in this context. 

But it's true that there are other graded lattices associated with a matroid, like the lattice of independent sets. So maybe names like f_vector_flats() and f_vector_independent_sets() are less ambiguous.

Cheers,

Rudi

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