Enumeration of ad-nilpotent $\frak b$-ideals for simple Lie algebras
  We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence. 
Christian Krattenthaler (Universit\"at Wien), Luigi Orsina, Paolo Papi   (Universit\`a di Roma "La Sapienza")