A combinatorial approach to the theory of pi-algebras and exponential growth
pp. 493-511
in: Henry Crapo, Domenico Senato (eds), Algebraic combinatorics and computer science, Berlin, Springer, 2001Abstract
The theory of Pi-algebras has been developed in the last decade mainly through combinatorial methods pertaining to the representation theory of the symmetric group in characteristic zero. These methods together with the study of the asymptotic behavior of a numerical sequence related to a PI-algebra have lead to the notion of the PIexponent of an algebra. Through the scale determined by the exponent many results have been obtained in the last few years shedding new light on the understanding of the polynomial identities of an algebra.