Fast Straightening Algorithm for Bracket Polynomials Based on Tableau Manipulations

Abstract

Straightening is the most fundamental symbolic manipulation in bracket algebra. Young's classical algorithm and White's more recent algorithm have poor performance in straightening bracket polynomials of degree >4. Rota's straightening algorithm based on Capelli operator is generally superior to the former two in speed, but still performs badly when the degree reaches 5. In this paper, a new operator is defined in bracket algebra based on tableau manipulations, and is simpler than Capelli operator. A new straightening algorithm is then proposed, and is superior to the above three algorithms by a speedup of two order of magnitude on average by testing over 500 examples in the past two years.