The r-Stifling numbers of the first and second kind count restricted permutations and respectively restricted partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic properties of these numbers, which in most cases generalize similar properties of the regular Stirling numbers, are explored starting...

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.

Requirements for Service Creation Environments Nikolaos Kosmas and Kenneth J. Turner Department of Computing Science University of Stirling Stirling, Great Britain fnko,[email protected] Abstract Service Creation Environments are the new frontiers in telecommunications. E cient and reliable service creation is vital towards the evolution of the telecommunication domain as we move into Intellig...

Jane Wilcock Department of Primary Care and Population Sciences, RFUCLMS, London, UK, Michelle Bryans Department of Clinical and Counselling Psychology, NHS Lanarkshire, East Kilbride, UK, Stephen Turner Dental Health Services Research Unit, Dundee, Scotland, UK, Ronan O’Carroll Department of Psychology, University of Stirling, Stirling, Scotland, UK, John Keady Northumbria University/for Demen...

Boris Baer,' ' Michiel B. Dijkstra," Ulrich G. Mueller, David R. Nash, and Jacobus J. Boomsma* ^Centre for Social Evolution, Department of Biology, University of Copenhagen, Universitetsparken 15, DK-2100 Copenhagen, Denmark, Centre of Excellence in Plant Energy Biology, Molecular and Chemical Sciences Building M316, The University of Western Australia, 35 Stirling Highway, 6009 Crawley, Wester...

In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that is relevant to the so-called Boson normal ordering problem. They provided a recurrence and, more recently, also offered a (fairly complex) combinatorial interpretation of these numbers. We show that by restricting the numbers somewhat (but still wide...

Chris McGlory, Amanda White, Caroline Treins, Barry Drust, Graeme L. Close, Don P. M. MacLaren, Iain T. Campbell, Andrew Philp, Simon Schenk, James P. Morton, and D. Lee Hamilton Health & Exercise Sciences Research Group University of Stirling, Stirling, United Kingdom; Department of Orthopaedic Surgery, University of California San Diego, La Jolla, California; Biomedical Sciences Graduate Prog...

Centre for Exploration Targeting, The University of Western Australia, M006, 35 Stirling Highway, Crawley, WA 6009, Australia; b School of Earth and Environment, The University of Western Australia, M006, 35 Stirling Highway, Crawley, WA 6009, Australia; Western Australian Organic and Isotope Geochemistry Centre, Curtin University, Perth, WA 6845, Australia; d The Institute of Earth Sciences, T...

We define a generalization of the Stirling numbers of the first and second kinds and develop a new rook theory model to give combinatorial interpretations to these numbers. These rook-theoretic interpretations are used to give a direct combinatorial proof that two associated matrices are inverses of each other. We also give combinatorial interpretations of the numbers in terms of certain collec...