On the Number of Partition Weights with Kostka Multiplicity One

@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}
}
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

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