Solving Schubert Problems with Littlewood-Richardson Homotopies Institutional Repository Document

abstract

• 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.

authors

• Sottile, Frank

author list (cited authors)

• Sottile, F., Vakil, R., & Verschelde, J.

citation count

• 0

complete list of authors

• Sottile, Frank||Vakil, Ravi||Verschelde, Jan

Book Title

• arXiv

publication date

• January 2010

keywords

• 65h10; 14n15, 14q99, 68w30
• Math.ag
• Math.na

Digital Object Identifier (DOI)

• 10.48550/arxiv.1001.4125