منابع مشابه
Characterizations of Transversal and Fundamental Transversal Matroids
A result of Mason, as refined by Ingleton, characterizes transversal matroids as the matroids that satisfy a set of inequalities that relate the ranks of intersections and unions of nonempty sets of cyclic flats. We prove counterparts, for fundamental transversal matroids, of this and other characterizations of transversal matroids. In particular, we show that fundamental transversal matroids a...
متن کاملOn ternary transversal matroids
Ingleton [8, p. 123] raised the question of characterizing the class of transversal matroids that are representable over some particular field F. He noted that when F = GF(2), this problem had already been solved by de Sousa and Welsh [6] who showed that the class of binary transversal matroids coincides with the class of graphic transversal matroids. The latter class had earlier been character...
متن کاملCharacterization of transversal matroids
Matroids are discrete structures that capture independence under many different flavours. Our focus here is split between affine independence and transversal set theory. It was proved by Edmonds and Fulkerson in 1965 that the set of partial transversals of a set system are the independent sets of a matroid. A first attractive feature of these matroids (thus called transversal matroids) is that ...
متن کاملTransversal Matroids and Strata on Grassmannians
1. Let Zk~ be the manifold of all nondegenerate complex k × n-matrices, k < n , let Gkn be the Grassmannian of k-dimensional subspaces in C~', and let ~r: Zkn -~ Gk, be the na tura l projection (7~(z) for z E Zk~ is the k-dimensional subspace of C ~ generated by the rows of z). For a matr ix z E Zkn denote by px(z) = pil...ik(z) the minor of z composed by the columns with indices from the set I...
متن کاملOn the critical exponent of transversal matroids
Brylawski [2] has shown that loopless principal transversal matroids have critical exponent at most 2. Welsh [4] asks if a similar result holds for all transversal matroids. We answer in the affirmative by proving that all loopless transversal matroids have critical exponent at most 2. The terminology used here for matroids will in general follow Welsh 131. A rank r transversal matroid M is rep...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0387087-4