Professor Peter J. Larcombe (Dept. Computing and Mathematics, University of Derby) will speak in the Algebra seminar on Wednesday, 23 November 2016, at 2:00pm (room JBL0C05, JBL Building, which is building 22 on the uni map). He will talk about Catalan Numbers and Catalan Polynomials: An Overview of Some Work in Discrete Mathematics.
Abstract: In this talk I will present some results from my work in discrete mathematics. Integer sequences whose (ordinary) generating functions satisfy a quadratic equation are common, and in any sequence instance the functional coefficients of the governing equation characterise a namesake family of polynomials. I will give some initial results for the general class of polynomials and then – in relation to the particular family of Catalan polynomials – present the algebraic execution of some numeric root finding schemes (including the classic Newton-Raphson and Halley algorithms) that are found to deliver non-linear polynomial identities; such identities – termed ‘auto-identities’, can be produced…
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