Abstract
A matroid of rank r on n elements is a positroid if it has a representation by an r by n matrix over R, each r by r submatrix of which has nonnegative determinant. Earlier characterizations of connected positroids and results about direct sums of positroids involve connected flats and non-crossing partitions. We prove another characterization of positroids of a similar flavor and give some applications of the characterization. We show that if M and N are positroids and the intersection of their ground sets is an independent set and a set of clones in both M and N, then the free amalgam of M and N is a positroid, and we prove a second result of that type. Also, we identify several multi-parameter infinite families of excluded minors for the class of positroids.
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