Global ETD Search

1	A Puzzle-Based Synthesis Algorithm For a Triple Intersection of Schubert Varieties Brown, Andrew Alexander Harold 28 January 2010 (has links) 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. Schubet Calculus Littlewood-Richardson rule Puzzle Synthesis Combinatorics and Optimization
2	A Puzzle-Based Synthesis Algorithm For a Triple Intersection of Schubert Varieties Brown, Andrew Alexander Harold 28 January 2010 (has links) 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. Schubet Calculus Littlewood-Richardson rule Puzzle Synthesis Combinatorics and Optimization
3	A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK Bellissimo, Michael Robert 08 June 2018 (has links) No description available. Mathematics partitions badness Rouquier Block representation theory combinatorics Brauer Graph diameter of a Brauer Graph partition theory Young Diagram decomposition matrix p-core abacus p-regular partitions Littlewood-Richardson Rule
4	On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group Trinh, Megan 08 June 2018 (has links) No description available. Mathematics mathematics partitions combinatorics Rouquier block abacus Young diagram weight quotient Littlewood-Richardson Rule Chuang-Tan Rule Brauer graphs hook length rim hook representation theory

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