 | ECS #25: Cycles set |
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1. Description
- permutations Sigma such that Sigma^4=Id
- degree n permutations of order dividing 4
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Set} \left( {\rm Union} \left( {\rm Cycle} \left( Z,{
\rm card}=1 \right) ,{\rm Cycle} \left( Z,{\rm card}=2 \right) ,{\rm
Cycle} \left( Z,{\rm card}=4 \right) \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -6\,{n}^{2}-11\,n-6-{n}^{3} \right) f \left( n
\right) + \left( -n-3 \right) f \left( n+2 \right) +f \left( n+4
\right) -f \left( n+3 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =1,f \left( 2 \right) =2,f \left( 3 \right) =4 \right\}
other formats
3.3. Asymptotics
4. Exponential generating function
\displaystyle
{{\rm e}^{x+1/2\,{x}^{2}+1/4\,{x}^{4}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).