Finite geometry and permutation groups: some polynomial links
نویسنده
چکیده
A matroid on a set E is a family I of subsets of E (called independent sets) with the properties • a subset of an independent set is independent; • if A and B are independent with |A| < |B|, then there exists x ∈ B \A such that A∪{x} is independent. The rank ρ(A) of a subset A of E is the common size of maximal independent subsets of A. Examples of matroids: • E is a family of vectors in a vector space, independence is linear independence; • E is a family of vectors in a vector space, independence is affine independence; • E is a family of elements in a field K, independence is algebraic independence over a subfield F ; • E is the set of edges of a graph, a set is independent if it is acyclic; • E is the index set of a family (Ai : i ∈ E) of subsets of X , a set I is independent if (Ai : i ∈ I) has a system of distinct representatives.
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