W&M ScholarWorks

Title

Combinatorially Derived Properties of Young Tableaux

Author

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

Date Thesis Awarded

3-2014

Document Type

Honors Thesis

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. Paper 1.
https://scholarworks.wm.edu/honorstheses/1