Cyclic sum
From AoPSWiki
A cyclic sum is a summation that cycles through all the values of a function and takes their sum, so to speak.
Rigorous definition
Consider a function 
. The cyclic sum 
is equal to
Note that not all permutations of the variables are used; they are just cycled through.
Notation
A cyclic sum is often specified by having the variables to cycle through underneath the sigma, as follows: 
. Note that a cyclic sum need not cycle through all of the variables.
A cyclic sum is also sometimes specified by 
. This notation implies that all variables are cycled through.
