Characteristic sequences of non-associative algebras

Abstract

In this paper, we provide the complete characterization of integer sequences that are characteristic sequences for general non-associative algebras, i.e., we determine the set of combinatorial properties which hold for all characteristic sequences and construct corresponding algebras for integer sequences satisfying them. The obtained information on characteristic sequences is then applied to investigate the realizability problem for the length function. In particular, we determine certain segment of values which are not realizable as values of the length function.