Algebra and geometry: Cyclic sieving on circular Dyck paths

  • Date: –16:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Samu Potka (KTH)
  • Organiser: Matematiska institutionen
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

Abstract: The cyclic sieving phenomenon was defined by Reiner, Stanton and White in 2004. The ingredients are a finite set X, a cyclic group C acting on X, and a polynomial f(q) with integer coefficients and satisfying f(1) = |X|. The triple (X, C, f(q)) is said to exhibit the cyclic sieving phenomenon if f(q) evaluated at certain roots of unity gives the number of elements of X fixed by powers of a generator of C. We will discuss this curious phenomenon and an example instance on circular Dyck paths (joint work with Per Alexandersson and Svante Linusson).