Ternary Positroids
arxiv(2024)
摘要
A positroid is an ordered matroid realizable by a real matrix with all
nonnegative maximal minors. Postnikov gave a map from ordered matroids to
Grassmann necklaces, for which there is a unique positroid in each fiber of the
map. Here, we characterize the ternary positroids and the set of matroids in
their respective fibers, referred to as their positroid envelope classes. We
show that a positroid is ternary if and only if it is near-regular, and that
all ternary positroids are formed by direct sums and 2-sums of binary
positroids and positroid whirls. We fully characterize the envelope classes of
ternary positroids; in particular, the envelope class of a positroid whirl of
rank-r contains exactly four matroids.
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