Difference between revisions of "Cyclic sum"
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A '''cyclic''' sum is a [[summation]] that cycles through all the values of a function and takes their sum, so to speak. | A '''cyclic''' sum is a [[summation]] that cycles through all the values of a function and takes their sum, so to speak. | ||
Revision as of 22:45, 4 February 2008
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.
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
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.