 | ECS #64: maps |
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1. Description
Injective partial maps (Borwein et al), (increasing subsequences in perms)
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Set} \left( {\rm Union} \left( {\rm Cycle} \left( Z
\right) ,{\rm Sequence} \left( Z,1\leq {\rm card} \right) \right)
\right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 2\,n+1+{n}^{2} \right) f \left( n \right) + \left( -4-
2\,n \right) f \left( n+1 \right) +f \left( n+2 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =2 \right\}
other formats
3.3. Asymptotics
4. Exponential generating function
\displaystyle
{{\rm e}^{\ln \left( \left( 1-x \right) ^{-1} \right) + \left( 1-x
\right) ^{-1}-1}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).