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Volume:3, Issue: 8, 2009 Page No: 571 - 577

International Journal of Engineering, Mathematical and Physical Sciences

ISSN: 2517-9934

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DOI:10.5281/zenodo.1334592 BibTeX JSON

On the Numbers of Various Young Tableaux

We demonstrate a way to count the number of Young tableau u of shape λ = (k, k,L, k) with | λ |= lk by expanding Schur function. This result gives an answer to the question that was put out by Jenny Buontempo and Brian Hopkins.
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References:
[1] J. Demmel and P. Koev, The accurate and efficient solution of a totally
positive generalized Vandermonde linear system, SIAM J. Matrix Anal.
Appl., 27(1)(2005), 142-152.
[2] Jenny Buontempo, Brian Hopkins, Tableau Cycling and Catalan
Numbers, INTEGERS: Electronic Journal of Combinatorial Number
Theory 7 (2007), #A45.
[3] Young-Ming Chen, Hsuan-Chu Li and Eng-Tjioe Tan, An Explicit
Factorization of Totally Positive Generalized Vandermonde Matrices
Avoiding Schur Functions, Applied Mathematics E-Notes, 8(2008),
138-147.