International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 243-249

Analysis of straightening formula

Devadatta M. Kulkarni

Department of Mathematics, Oakland University, Rochester Michigan 48063, USA

Received 23 March 1987

Copyright © 1988 Devadatta M. Kulkarni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The straightening formula has been an essential part of a proof showing that the set of standard bitableaux (or the set of standard monomials in minors) gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as an integral linear cobmbination of standard bitableaux. In this paper we analyse the exchanges in the process of straightening a nonstandard pure tableau of depth two. We give precisely the number of steps required to straighten a given violation of a nonstandard tableau. We also characterise the violation which is eliminated in a single step.