Speaker: Richard Ehrenborg, University of Kentucky

Title: The descent set polynomial revisited

Abstract: We explore cyclotomic factors in the descent set polynomial Q_n(t), which was introduced by Chebikin, Ehrenborg, Pylyavskyy and Readdy. We obtain large classes of factors of the form Φ_2s or Φ_4s where s is an odd integer, with many of these being of the form Φ_2p where p is a prime. We also show that if Φ₂ is a factor of Q_2n(t) then it is a double factor. Finally, we give conditions for an odd prime power q = p^r for which Φ_2p is a double factor of Q_2q(t) and of Q_q+1(t). This is joint work with Brad Fox.