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arxiv: 1803.01726 · v1 · pith:BWURLQMZnew · submitted 2018-03-05 · 🧮 math.CO

An algorithm to construct the Le diagram associated to a Grassmann necklace

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keywords grassmannalgorithmdiagramnecklaceeasilypositroidalreadyassociated
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Le diagrams and Grassmann necklaces both index the collection of positroids in the nonnegative Grassmannian $Gr_{\geq 0}(k,n)$, but they excel at very different tasks: for example, the dimension of a positroid is easily extracted from its Le diagram, while the list of bases of a positroid is far more easily obtained from its Grassmann necklace. Explicit bijections between the two are therefore desirable. An algorithm for turning a Le diagram into a Grassmann necklace already exists; in this note we give the reverse algorithm.

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