1Department of Behavioral Sciences, Faculty of General Medicine, University of Szeged, Szeged, Hungary 2Royal Ottawa Mental Health Centre, Institute of Mental Health Research and Department of Psychiatry, University of Ottawa, Ottawa, Canada 3Department of Psychology, University of Stirling, Stirling, Scotland, UK 4Research and Evaluation Unit, Women’s and Children’s Hospital and School of Paed...

The generalized Stirling numbers introduced recently [11, 12] are considered in detail for the particular case s = 2 corresponding to the meromorphic Weyl algebra. A combinatorial interpretation in terms of perfect matchings is given for these meromorphic Stirling numbers and the connection to Bessel functions is discussed. Furthermore, two related q-polynomial identities are derived.

Chen, J-C. (corresponding author, [email protected] ), Greenwood , S. ([email protected] ), Chen, C-T. ([email protected]), Jump, A.S. ([email protected]) Department of Forestry, National Pingtung University of Science and Technology, 1 Hseuh Fu Road, Nei Pu Hsiang, Pingtung 912, Taiwan; Biological and Environmental Sciences, School of Natural Sciences, University of ...

We exploit a bijection between plane recursive trees and Stirling permutations; this yields the equivalence of some results previously proven separately by different methods for the two types of objects as well as some new results. We also prove results on the joint distribution of the numbers of ascents, descents and plateaux in a random Stirling permutation. The proof uses an interesting gene...

We describe the relation between graph decompositions into walks and the normal ordering of differential operators in the n-th Weyl algebra. Under several specifications, we study new types of restricted set partitions, and a generalization of Stirling numbers, which we call the λ-Stirling numbers.

We prove an identity for sums of products of an arbitrary fixed number of Stirling numbers of the second kind; this can be seen as a generalized convolution identity. As a consequence we obtain two polynomial identities that also involve Stirling numbers of the second kind.

Starting with divided di erences of binomial coe cients, a class of multivalued polynomials (three parameters), which includes Bernoulli and Stirling polynomials and various generalizations, is developed. These carry a natural and convenient combinatorial interpretation. Some particular calculations are done and several factorization results are proven and conjectured.

We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural three-parameter generalization of the well-known Eulerian numbers. We give the generating function for this new class of numbers and, in the simplest cases, we...