 | ECS #19: Set partitions |
| Introduction | Examples | Search | Submit | Help | Links |
1. Description
- Set partitions with all blocks of size <=4
- the partition function G(n,4)
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Set} \left( {\rm Union} \left( {\rm Set} \left( Z,{\rm
card}=1 \right) ,{\rm Set} \left( Z,{\rm card}=2 \right) ,{\rm Set}
\left( Z,{\rm card}=3 \right) ,{\rm Set} \left( Z,{\rm card}=4
\right) \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{3}-6\,{n}^{2}-11\,n-6 \right) f \left( n
\right) + \left( -18-3\,{n}^{2}-15\,n \right) f \left( n+1 \right) +
\left( -18-6\,n \right) f \left( n+2 \right) +6\,f \left( n+4 \right)
-6\,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) =5 \right\}
other formats
3.3. Asymptotics
4. Exponential generating function
\displaystyle
{{\rm e}^{x+1/2\,{x}^{2}+1/6\,{x}^{3}+1/24\,{x}^{4}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).