For a set of variables X 1 , … , X n {\displaystyle {}X_{1},\ldots ,X_{n}} and an n {\displaystyle {}n} -tuple ( ν 1 , … , ν n ) ∈ N n {\displaystyle {}(\nu _{1},\ldots ,\nu _{n})\in \mathbb {N} ^{n}} , an expression of the form X 1 ν 1 ⋯ X n ν n {\displaystyle {}X_{1}^{\nu _{1}}\cdots X_{n}^{\nu _{n}}} is called a monomial in the X i {\displaystyle {}X_{i}} .
and an
-tuple
,
an expression of the form 
is called a monomial in the 
.