"Almost mean" of a set of integer I have three integers $(a, b, c)$ (but this can be generalized to any size). I want to redistribute the sum $a+b+c$ as equally as possible between three variables. In our case, we have three cases:
If $a+b+c=3k$, then the solution is $(k, k, k)$.
If $a+b+c=3k+1$, then the solution is $(k, k, k+1)$.
If $a+b+c=3k+2$, then the solution is $(k+1, k+1, k)$.
Does this notion have a name in mathematics?
Any references?
Thanks.
 A: This paper explains a slight variant of Euclid's algorithm that solves this problem, and says that these near-uniform distributions occur in traditional musical rhythms.
This article uses the term "Euclidean rhythm", but maybe that doesn't make sense in a broader context than music.
A: From a graph theoretical perspective, there exists a specificly named graph called a Turan Graph labeled in writing as $T(n,r)$ (the turan graph on $n$ vertices subdivided into $r$ camps).  It has the special property of being the graph with the most number of edges which does not contain a clique of size $r+1$.  As far as I can see, they did not name the process used in separating the integers, but rather spell it out that for $n$ vertices and $r$ camps, there will be $(n~\text{mod}~r)$ subsets of size $\lceil n/r\rceil$ and $n - (n~\text{mod}~r)$ subsets of size $\lfloor n/r\rfloor$.

A: This really is just the "division algorithm." Let $m$ be the sum you want, and $n$ be the number of variables.
Use the division algorithm to write $m=nq+r$ with $q$ the quotient and $0\leq r<n$ the remainder. Then you can write $m$ as the sum of $r$ instances of $q+1$ and $n-r$ instances of $q$.
