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Commuting Polynomials and Generalized Odd Polynomials

by

Karl Zimmermann
Union College

February 8, 2010
4:30 pm
Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:15


Abstract:

It is well known that polynomials commute under addition and multiplication, that is, $f + g = g + f$ and $fg = gf$ for polynomials $f$ and $g$. On the other hand, polynomials may not commute under function composition. In fact, it is likely that $f\circ \ne g\circ f$. In the first part of this talk, we’ll look at polynomials that do commute under composition. Then, we’ll review the concepts of even polynomial and odd polynomial and generalize the latter. Finally we’ll see a connection between these generalized odd polynomials and polynomials that commute under composition.

Homework: Try to find some examples of polynomials that commute under composition!!


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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