The Dotted straightening algorithm

Abstract

If a homogeneous bracket polynomial is antisymmetric in certain subsets of its points, then it can be represented in an abbreviated form called a dotted bracket expression. These dotted bracket expressions lead to a more compact expression in terms of tableaux than the usual representation. Consequently, we can derive a much more efficient straightening algorithm than the ordinary one for bracket polynomials already given in dotted form. This dotted straightening algorithm gives precisely the same result as the ordinary one, and preserves the dotted property at every step.