We give combinatorial proofs of q-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz’s identity, a new proof of the q-Frobenius identity of Garsia and Remmel and of Ehrenborg’s Hankel q-Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.

s of Communications 565th Meeting of the Biochemical Society University of Stirling 9 and 10 September 1976 CONTROL M ECH AN ISMS I N D I FFER ENTl AT1 ON AND DEVELOPMENT: a Colloquium organized by L. Stevens (Stirling) Control of Cell Differentiation in the Cellular Slime Mould Dictyostelium discoideum

The Legendre-Stirling numbers were discovered in 2002 as a result of a problem involving the spectral theory of powers of the classical secondorder Legendre differential expression. Specifically, these numbers are the coefficients of integral composite powers of the Legendre expression in Lagrangian symmetric form. Quite remarkably, they share many similar properties with the classical Stirling...

Abstract. We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind JS(n+ k, n; z) by generalizing the analogous results for the Stirling and Legendre-Stirling numbers. More precisely, letting JS(n + k, n; z) = pk,0(n) + pk,1(n)z + · · ·+ pk,k(n)z , we show that (1− t) ∑ n≥0 pk,i(n)t n is a polynomial in t with nonnegative integral coefficients and provid...

Stirling numbers of the second kind and Bell numbers for graphs were defined by Duncan and Peele in 2009. In a previous paper, one of us, jointly with Nyul, extended the known results for these special numbers by giving new identities, and provided a list of explicit expressions for Stirling numbers of the second kind and Bell numbers for particular graphs. In this work we introduce q-Stirling ...

a straightforward approach for identifyingmultiple spatial movement patterns KevinMorelle* , Nils Bunnefeld, Philippe Lejeune andStephenA.Oswald BIOSEDepartment, Gembloux Agro-Bio Tech, University of Li ege, passage des d eport es 2, 5030Gembloux, Belgium; Biological and Environmental Sciences, School of Natural Sciences, University of Stirling, Stirling FK9 4LA, UK; and Division of Science, Pe...

a Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, UK b Division of Neuroscience and Biomedical Systems, IBLS University of Glasgow West, Medical Building Glasgow, G12 8QQ, UK c Department of Mathematics, Centre for Neural Networks, King’s College London, London, UK d Centre for Theoretical and Computational Neuroscience, University of Plymouth, Plymout...