Hi,everyone .Let  A a no-empty set ,suppose  A is finite and let  n ,natural \neq 0 , its cardinality ,let  k a natural number \neq 0 : we say every ordinate  k -upla  ( a_{1}...a_{k}) is a disposition with repetition of class k of  A where  a_{i} \in A .To define a combination with repetition of class  k of  A i gave the following deinition: let  ( a_{1}...a_{k}) ,  ( b_{1}...b_{k}) two dispositions with repetition of class  k of  A .We say  ( a_{1}...a_{k}) and  ( b_{1}...b_{k}) are "of the same type" if \{a_{1}...a_{k}\} =\{b_{1}...b_{k}\} , and ,set \{a_{1}...a_{k}\}=\{c_{1}...c_{r}\}  ,where r is the cardinality of  \{a_{1}...a_{k}\} , we have  \forall i\in  \{1,...,r\}  \sharp ( \{j \in\{1,...,k\}\mid a_{j}=c_{i} \} = \sharp ( \{j \in\{1,...,k\}\mid b_{j}=c_{i} \}  . So we can consider the following set  R= \{ (a,b) \in \{ every disposition with repetion of class k of  A \}^{2}\mid  a and  b are "of the same type"  \} and observe R is an equivalence relation on \{ every disposition with repetiton of class k of  A } ,so we can say \forall  disposition with repetition of class k of  A } ,  a , the equivalence class of  a on \{ every disposition with repetition of class k of  A } modulo  R is a combination with repetition of class k of  A .Is this definition already used ?