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(N,
x), ...,
occ(N,
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.