|This is an AoPSWiki Word of the Week for February 4-11|
A cyclic sum is a summation that cycles through all the values of a function and takes their sum, so to speak.
Consider a function . The cyclic sum is equal to
Note that not all permutations of the variables are used; they are just cycled through.
If a summation is specified without additional arguments, it is generally assumed to be a cyclic sum. A cyclic sum can also be 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.