# Restricted Stirling and Lah number matrices and their inverses

@article{Engbers2016RestrictedSA, title={Restricted Stirling and Lah number matrices and their inverses}, author={John Engbers and David Galvin and Clifford D. Smyth}, journal={J. Comb. Theory, Ser. A}, year={2016}, volume={161}, pages={271-298} }

Given $R \subseteq \mathbb{N}$ let ${n \brace k}_R$, ${n \brack k}_R$, and $L(n,k)_R$ be the number of ways of partitioning the set $[n]$ into $k$ non-empty subsets, cycles and lists, respectively, with each block having cardinality in $R$. We refer to these as the $R$-restricted Stirling numbers of the second and first kind and the $R$-restricted Lah numbers, respectively. Note that the classical Stirling numbers of the second kind and first kind, and Lah numbers are ${n \brace k} = {n \brace… CONTINUE READING

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