Abstract In this paper we study natural reconfiguration spaces associated to the problem of distributing a fixed number resources labeled nodes tree network, so that no node is left empty. These turn out be cubical complexes, which can thought as higher-dimensional geometric extensions combinatorial Stirling partitioning set named objects into non-empty parts. As our main result, prove these co...

Stirling JW, Woods A. Transmission electron microscopy: diagnostic applications. In: Bancroft JD, Gamble M, eds. Theory and Practice of Histological Techniques, 5th ed. London: Churchill Livingstone; 2002:701-728. JOHN W STIRLING Principal Medical Scientist, Electron Microscope Unit, Anatomical Pathology, Flinders Medical Centre, Bedford Park SA 5042 Australia and Co-Convener RCPA QAP EM progra...

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

This paper studies the generalizations of the Stirling numbers of both kinds and the Lah numbers in association with the normal ordering problem in the Weyl algebra W = 〈x,D|Dx − xD = 1〉. Any word ω ∈ W with m x’s and n D’s can be expressed in the normally ordered form ω = xm−n ∑ k>0 { ω k } xkDk, where { ω k } is known as the Stirling number of the second kind for the word ω. This study consid...

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...

Denote by Σnm the sum of the m-th powers of the first n positive integers 1m + 2m + . . .+ nm. Similarly let Σrnm be the r-fold sum of the m-th powers of the first n positive integers, defined such that Σn = nm, and then recursively by Σn = Σr1m+Σr2m+ . . .+Σrnm. During the early 17th-century, polynomial expressions for the sums Σrnm and their factorisation and polynomial basis representation p...