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On the Numbers of Various Young Tableaux

Authors: Hsuan-Chu Li

Abstract:

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.

Keywords: Young tableau, Schur function.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334592

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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.