##  [Burnside's Lemma](/burnsides-lemma) 

  ##  [Burnside's Lemma](https://mathlogic.quantumdictionary.io/burnsides-lemma-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A counting technique that computes the number of distinct orbits (inequivalent configurations) of a finite set under the action of a finite group by averaging the number of fixed points of group elements.

 

 

 

 

 





 

 



 ##  [Burnside's Lemma](https://puremath.quantumdictionary.io/burnsides-lemma-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A counting principle for a finite group action on a finite set that computes the number of distinct orbits as the average, over group elements, of the number of points fixed by each element.

 

 

 

 

 





 

 



 ##  [Burnside's Lemma](https://algebra.quantumdictionary.io/burnsides-lemma-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A counting lemma that computes the number of distinct orbits of a finite set under the action of a finite group by averaging the number of fixed points of group elements.