Solving schubert problems with Littlewood-Richardson homotopies Conference Paper uri icon

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. Copyright 2010 ACM.

name of conference

  • Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation

published proceedings

  • Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation

author list (cited authors)

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

citation count

  • 4

complete list of authors

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

publication date

  • July 2010