Number of vertices in Gelfand-Zetlin polytopes
  We discuss the problem of counting vertices in Gelfand-Zetlin polytopes. Namely, we deduce a partial differential equation with constant coefficients on the exponential generating function for these numbers. For some particular classes of Gelfand-Zetlin polytopes, the number of vertices can be given by explicit formulas. 
Pavel Gusev, Valentina Kiritchenko, and Vladlen Timorin
math.CO