Mathematical Structures Defined by Identities II

Details Mathematical Structures Defined by Identities II Mathematical Structures Defined by Identities II

2010-09-06

arxiv.org/abs/1009.1006v1

Mathematics

Rings and Algebras

6 pages

Scientific paper

In our paper arXiv: math.RA/0110333 v1 Oct 2001 we showed that the number of algebras defined by a binary operation satisfying a formally irreducible identity between two n-iterates is O( e^{-n/16}S_{n}^{2} for n --> infinity, S_{n} being the nth-Catalan number. This was proved by using exclusively the series of tableaux A_{n}. By using also the series of tableaux B_{n}, we now sharpen this result to O{(n+2)/n|e^{-n/16}-2/n)|S_{n}^{2}}

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