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Seminar Details

Bijective Proofs in Partition Theory

  • Start Date: July 26, 2007
  • Event Start Time: 12:00 PM
  • Event End Time: 1:00 PM
  • Organizers: Christine Agnese
  • Seminar Series: REU Seminar
  • Presenter(s): Andrew Baxter - Rutgers University
  • Event Location: DIMACS Seminar room
  • Abstract: A partition of an integer N is a nonincreasing sequence of nonnegative integers which sum to N. In other words, a way to write N as the sum of other numbers without regard to order. The subject of partition theory counts the number of partitions of an integer. Things really get interesting when you start restricting the kinds of addends you're allowed to use, such as only using odd addends or requiring that all addends be distinct. While analytic proofs involving generating functions (which happen to be q-series) are common, the most satisfying proofs in the subject are bijective proofs. I will summarize some of the more interesting bijections, as well as known identities in need of bijective proofs.