Highly Influenced

5 Excerpts

@article{Gates2012OnTN, title={On the Number of Partition Weights with Kostka Multiplicity One}, author={Zachary Gates and Brian Goldman and C. Ryan Vinroot}, journal={Electr. J. Comb.}, year={2012}, volume={19}, pages={P52} }

- Published in Electr. J. Comb. 2012

Given a positive integer n, and partitions λ and μ of n, let Kλμ denote the Kostka number, which is the number of semistandard Young tableaux of shape λ and weight μ. Let J(λ) denote the number of μ such that Kλμ = 1. By applying a result of Berenshtein and Zelevinskii, we obtain a formula for J(λ) in terms of restricted partition functions, which is recursive in the number of distinct part sizes of λ. We use this to classify all partitions λ such that J(λ) = 1 and all λ such that J(λ) = 2. We… CONTINUE READING