- (1)
- (2) and
*M*is less than*N*with respect to the graded lex order

- (a) (we set and ) for
- (b)
*occ*(*M*,*V*) is the sum of*occ*(*M*,*v*) for all .

where is
``«'' if *j* is one of the 's and
is ``<'' otherwise.

Note that if the collection of subsets is
the empty set, then
the multigraded lex order is graded lex and if
the collection of subsets is
{1, 2, ..., *n* - 1},
then the multigraded lex order is a pure lex order.

As another example, a multigraded lex order for monic monomials in
*a*, *b*, *c*, *d* and *e* such that *a*<*b*<*c*<*d*<*e* can be specified
by specifying the set {2, 4}.
This multigraded lex order would be denoted
*a < b « c < d « e*

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Wed Jul 3 10:27:42 PDT 1996