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AN ALGORITHM TO CONSTRUCT THE LE DIAGRAM ASSOCIATED TO A GRASSMANN NECKLACE

Part of: Designs and configurations Algebraic combinatorics

Published online by Cambridge University Press:  18 January 2019

SUSAMA AGARWALA  and
SIÂN FRYER
SUSAMA AGARWALA
Affiliation:
Johns Hopkins Applied Physics Lab, Laurel, MD 20723, USA e-mail: susama.agarwala@jhuapl.edu
SIÂN FRYER*
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106-3080, USA e-mail: fryer@ucsb.edu
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Abstract

Le diagrams and Grassmann necklaces both index the collection of positroids in the nonnegative Grassmannian Gr≥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.

MSC classification

Primary: 05B35: Matroids, geometric lattices
Secondary: 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 85 - 91
Creative Commons
This is a work of the U.S. Government and is not subject to copyright protection in the United States
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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