Solving Schubert Problems with Littlewood-Richardson Homotopies

Details Solving Schubert Problems with Littlewood-Richardson Homotopies Solving Schubert Problems with Littlewood-Richardson Homotopies

2010-01-23

arxiv.org/abs/1001.4125v1

Mathematics

Numerical Analysis

Extended abstract. 14 pages

Scientific paper

We present a new numerical homotopy continuation algorithm for finding all solutions to Schubert problems on Grassmannians. This Littlewood-Richardson homotopy is based on Vakil's geometric proof of the Littlewood-Richardson rule. Its start solutions are given by linear equations and they are tracked through a sequence of homotopies encoded by certain checker configurations to find the solutions to a given Schubert problem. For generic Schubert problems the number of paths tracked is optimal. The Littlewood-Richardson homotopy algorithm is implemented using the path trackers of the software package PHCpack.

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