Espousable societies and infinite matroids
نویسنده
چکیده
Given a society Γ = (M, W, K), where M , W are disjoint sets and K ⊆M×W , and a matroid T on M , a T-espousal of Γ is an injective partial function E : M → W such that E ⊆ K and domE is spanning in T. The problem of characterizing Tespousable societies is a generalization of characterizing systems of matroids with disjoint bases. Wojciechowski [15] formulated a criterion for a society Γ = (M, W, K) to be P(M)espousable, where P(M) is the matroid on M consisting of all subsets of M . In this paper, we generalize this criterion to the case when T is an arbitrary matroid on M , and we prove that the obtained criterion is necessary for Γ to be T-espousable.
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