Peter Larcombe Email & Phone Number

Research Profile My research output spans the entire spectrum of past and present research interests. It currently totals 70+ journal papers (published or accepted), together with various conference/symposium/workshop papers, professional magazine/journal articles, book chapters, etc. My publications listing comprises the results of new and original pieces of research in discrete and applied mathematics (and occasionally works of both a historical and pedagogical nature). My work over the last fifteen years or so involves, in essence, the creation/identification and solution of a variety of mathematical problems within combinatorics and discrete mathematics which broadly address various aspects of integer and complex recurrence sequences, hypergeometric functions/identities, generating functions and binomial sums/identities. While I naturally undertake some elements of research on an ad hoc basis, my main concentrated contribution here has been in the area of sequences, as evidenced in particular by two integer sequences which have been established and formally recognised by name - the so called Catalan-Larcombe-French and Fennessey-Larcombe-French sequences. Through past and ongoing work I have also opened up and begun to explore a new area of discrete mathematics based on the notion of an Iterated Generating Function. An I.G.F. - arising from some input/output rule governing general (real or complex) polynomials - is an iterative construct which generates a sequence through the coefficients of its terms as the computations progress. Finally, a longstanding construct (a so called Horadam sequence) has been re-examined and new results found, particularly with reference to periodicity.