On the \(r\)-derangements of type B

István Mező1, Victor H. Moll2, José Ramírez3, Diego Villamizar2
1School of Mathematics and Statistics, Nanjing University of Information Science and Tech- nology, Nanjing, 210044, P. R. China
2Department of Mathematics, Tulane University, New Orleans, LA 70118
3Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

Abstract

Extensions of a set partition obtained by imposing bounds on the size of the parts and the coloring of some of the elements are examined. Combinatorial properties and the generating functions of some counting sequences associated with these partitions are established. Connections with Riordan arrays are presented.