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

Abstract

AbstractLe 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.