This thesis develops an algorithm for the Schubert calculus of the Grassmanian.
Specifically, we state a puzzle-based, synthesis algorithm for a triple
intersection of Schubert varieties. Our algorithm is a reformulation of the
synthesis algorithm by Bercovici, Collins, Dykema, Li, and Timotin. We replace
their combinatorial approach, based on specialized Lebesgue measures,
with an approach based on the puzzles of Knutson, Tao and Woodward.
The use of puzzles in our algorithm is beneficial for several reasons, foremost
among them being the larger body of work exploiting puzzles. To understand
the algorithm, we study the necessary Schubert calculus of the Grassmanian
to define synthesis. We also discuss the puzzle-based Littlewood-Richardson
rule, which connects puzzles to triple intersections of Schubert varieties. We
also survey three combinatorial objects related to puzzles in which we include
a puzzle-based construction, by King, Tollu, and Toumazet, of the well
known Horn inequalities.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/5010 |
| Date | 28 January 2010 |
| Creators | Brown, Andrew Alexander Harold |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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