A polynomial generalization of some associated sequences related to set partitions
The authors introduce a family of polynomials \(w_{m}^{a,b,c,d} (n,k)\) which for different choices of the parameters \(a,b,c,d\) generate different associate sequences of special numbers. Thus, for example, we have \(w_{1}^{0,1,0,1} (n,k)=S(n,k)\), the classical Stirling numbers of the second kind and \(w_{1}^{0,1,1,0} (n,k)\)are the unsigned Stirling numbers of the first kind. Also, \(w_{1}^{0,1,1,1} (n,k)=L(n,k)\) are the Lah numbers. For \(m\geq 1\) one comes to the associated Stirling and Lah numbers. The paper studies various properties of the above polynomials and provides combinatorial interpretations.
scientific article; zbMATH DE number 6850233
scientific article