Bijections between generalized Catalan families of types A and C
  Motivated by the relation holding for the m-generalized Catalan numbers of type A and C, the connection between dominant regions of the m-Shi arrangement of type A and C is investigated. In the same line of thought, a bijection between mn+1 copies of each m-Dyck path of height n and the set of NE lattice paths inside an n times mn rectangle is provided. 
Myrto Kallipoliti, Eleni Tzanaki
math.CO