Seminar:

Spring, Thursdays, Blocker 506A, 4:00-4:50 PM


Date: April 27

"  "Interpolants and Necklaces" "
  Taylor Brysiewicz  

Abstract

Graphs of Taylor polynomials provide good approximations of graphs of other functions in the plane. However, if we generalize graphs of Taylor polynomials to parametric curves of the form (x(t),y(t)) for polynomials x and y of degrees n and m we can approximate even better. Although Taylor polynomials are unique, these generalized interpolants are often not. In this talk we count the number of such interpolants to be the same as the number of combinatorial necklaces on n white beads and m black beads.