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

2018/03/05 by Susama Agarwala, Agarwala, Susama, Siân Fryer +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1803.01726

openalex publication_date 2018/03/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

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

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