For a monic monomial *M* and a variable *v* ,
let *occ*(*M*,*v*) be the number of occurrences of
*v* in *M*. (For example,
*occ*(*a b c d c*,*a*) = 1,
*occ*(*a b c d c*,*b*) = 1,
*occ*(*a b c d c*,*c*) = 2,
*occ*(*a b c d c*,*d*) = 1 and
*occ*(*a b c d c*,*e*) = 0.)

Let *M* and *N* be monic monomials in the variables
*x* ,
...,
*x* .
*M* is less than *N* with respect to the pure
lex order
*x*
«
*x*
« ... «
*x*
if one of the
following two conditions holds.

- (
*occ*(*M*,*x*), ...,*occ*(*M*,*x*)) < (*occ*(*N*,*x*), ...,*occ*(*N*,*x*)) - (
*occ*(*M*,*x*), ...,*occ*(*M*,*x*)) = (*occ*(*N*,*x*), ...,*occ*(*N*,*x*)) and*M*is less than*N*with respect to the graded lex order*x*<*x*< ... <*x*.

Wed Jul 3 10:27:42 PDT 1996