Evaluation and spanning sets of confluent Vandermonde forms

  title={Evaluation and spanning sets of confluent Vandermonde forms},
  author={Denis K. Sunko},
  journal={Journal of Mathematical Physics},
  • D. Sunko
  • Published 1 August 2022
  • Mathematics
  • Journal of Mathematical Physics
An arbitrary derivative of a Vandermonde form in N variables is given as [ n1⋯ n N], where the ith variable is differentiated N − n i − 1 times, 1 ≤ n i ≤ N − 1. A simple decoding table is introduced to evaluate it by inspection. The special cases where 0 ≤ n i+1 − n i ≤ 1 for 0 < i < N are in one-to-one correspondence with ribbon Young diagrams. The respective N! standard ribbon tableaux map to a complete graded basis in the space of S N-harmonic polynomials. The mapping is realized as an… 

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