Analysis of straightening formula (Q1118591)

The straightening formula of \textit{G. Rota}, \textit{P. Doubillet} and \textit{J. Stein} [Stud. Appl. Math. 53, 185-216 (1974; Zbl 0426.05009)] has been an integral part of the theorem showing that the set of standard bitableux form a free basis of the polynomial ring in a matrix of indeterminates over a field. \textit{S. Abhyankar} [Combinatorie des tableaux de Young, variétés déterminantielles et calcul de fonctions de Hilbert; Nice Lect. Notes by A. Galligo; Univ. E. Polytec. Torino: Rend. Sem. Mat. (1985)] gives a proof of the mentioned theorem by explicitly counting the dimension of a vector space generated by all the standard bitableaux of area V and length less than or equal to p. In the paper under review, the author analyses the results of Abhyankar. He gives an exact number of steps required to eliminate the violation from all unitableaux obtained in the straightening.