** 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 Φ_{2} 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.