Title

Combinatorially Derived Properties of Young Tableaux

Author

James R. Janopaul-Naylor, College of William and MaryFollow

Date Thesis Awarded

3-2014

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Ryan Vinroot

Committee Members

Paul Heideman

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 K_λμ = 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.

Recommended Citation

Janopaul-Naylor, James R., "Combinatorially Derived Properties of Young Tableaux" (2014). Undergraduate Honors Theses. William & Mary. Paper 1.
https://scholarworks.wm.edu/honorstheses/1

Creative Commons License

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