Date Thesis Awarded

3-2014

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Ryan Vinroot

Committee Member

Paul Heideman

Committee Member

Gexin Yu

Abstract

We examine properties of Young tableaux of shape λ and weight μ or of shape {λ(i)}, a sequence of partitions. First we use combinatorial arguments to re- derive results about individual tableaux from Behrenstein and Zelevinskii regard- ing Kostka numbers and from Gates, Goldman, and Vinroot regarding when the weight μ on a tableau of shape λ is the unique weight with Kλμ = 1. Second we generalize these results to sequences of tableaux. Specifically we show under what conditions is K{λ(i)}μ = 1 for a sequence of partitions {λ(i)} and weight μ and when is there a unique weight μ for a sequence of partitions with K{λ(i)}μ = 1.

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