Events - Colloquia & Seminars

CCIS Colloquium Spring 2008

Combinatorial identities, and visualizing recursion

Speaker: Erich Neuwirth

Affiliation: University of Vienna

Date: Monday, January 14, 2008

Talk: 12:00 p.m., 366 WVH

Abstract

Many basic combinatorics problems share a recursion structure related to Galton's board (or Pascal's triangle), described by

F(n,k)=a(n-1,k)F(n-1,k)+b(n-1,k-1)F(n-1,k-1)

Visualizing this structure can help understanding the properties of then combinatorial functions. These basic problems have recursion depth of 1, but it is possible to extend the depth and generalize the results from "short" recursion to "long" recursion. All these results represent combinatorial functions as infinite matrices, and the in this context combinatorial identities are represented as matrix equations about matrix multiplication and inversion.

Brief Biography

Erich Neuwirth is a Professor of Statistics and Computer Science at the University of Vienna. He is a member of the Data Analysis and Computational Systems Group in the Faculty of Computer Science. His research interests span combinatorics, statistical modeling, analysis and forecasting, use of spreadsheets as a tool for mathematical education, functional programming in education, mathematics and music. He received the European Academic Software Award in 1996 for his multimedia document about the mathematical foundations of musical temperaments.

For more information contact: Rachel Kalweit - rachelb@ccs.neu.edu