Mathematics – Combinatorics
Scientific paper
2010-07-29
Exclusively published in the electronic journal "The Personal Journal of Shalosh B. Ekhad and Doron Zeilberger" ( http://www
Mathematics
Combinatorics
3 pages. Accompanied by the Maple package http://www.math.rutgers.edu/~zeilberg/tokhniot/HOOKER . Extensive output files can
Scientific paper
This is an etude in experimental semi-rigorous (rigorizable!) mathematics. The leading asymptotics was brilliantly derived by Allan Berele and Amitai Regev for general hooks H(k,l) and general powers z, but what about more refined asymptotics? For small k and l, one can "guess" a linear recurrence (since we live in the holonomic ansatz) and using the Birkhoff-Trjitzinsky method, beautifully implemented in Doron Zeilberger's Maple package AsyRec (that has been incorporated into the present Maple package), we computed amazing refined asymptotics, that confirm, with a vengeance, the Berele-Regev asymptotic formula, and especially the impressive constant in front!
Ekhad Shalosh B.
Regev Amitai
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