• Park, H.G. ;
  • Yoon, D.S. ;
  • Park, S.H.
  • Published : 1997.02.01


The enumeration of various classes of paths in the real plane has an important implications in the area of combinatorics wit statistical applications. In 1887, D. Andre [3, pp. 21] first solved the famous ballot problem, formulated by Berttand [2], by using the well-known reflection principle which contributed tremendously to resolve the problems of enumeration of various classes of lattice paths in the plane. First, it is necessary to state the definition of NSEW-paths in the palne which will be employed throughout the paper. From [3, 10, 11], we can find results concerning many of the basics discussed in section 1 and 2.


ballot number;Catalan number;dyck language;dyck path;lattice path


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