# 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. | ||

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==Notation== | ==Notation== | ||

− | + | A cyclic sum is often specified by having the variables to cycle through underneath the sigma, as follows: <math>\sum_{a,b,c}\frac{ab}{cd}</math>. Note that a cyclic sum need not cycle through all of the variables. | |

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+ | A cyclic sum is also sometimes specified by <math>\sum_{cyc}</math>. This notation implies that all variables are cycled through. | ||

==See also== | ==See also== |

## Revision as of 17:42, 12 February 2008

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.