Combinations with ripetition

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