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Seminar Details

Mobius Functions on Partially Ordered Sets

  • Start Date: July 24, 2008
  • Event Start Time: 12:00 PM
  • Event End Time: 1:00 PM
  • Organizers: Christine Agnese
  • Seminar Series: REU Seminar
  • Presenter(s): Aaron Jaggard - Rutgers University
  • Event Location: DIMACS Seminar room
  • Abstract: A result from number theory says that if f and g are two functions such that f(n) is always the sum of g(d) over the divisors d of n, then g(n) may be expressed as a (slightly more complicated sum) involving f(d), where d again ranges over the divisors of n; this is called "Mobius inversion.'' In discrete math, the "Principle of Inclusion-Exclusion'' tells us that the size of the union of two finite sets equals the sum of their sizes minus the size of their intersection, and it also gives us a general formula for the size of the union of k finite sets. It turns out that these results are related to each other through a more general theory of functions defined on certain classes of posets. Here we present a self-contained survey of these elegant connections.