PLANE LANGUAGES AND THEIR PROPERTIES

In this paper we study the Generalized Parikh Vector of words over three letter alphabet. For S = {a, b, c} the GPVs of words lie in the tetrahedron whose vertices are (1, 0, 0), (0, 1, 0), (0, 0, 1) and (0, 0, 0). All GPVs of words of equal length lie on the same plane. Plane languages and their language theoretical properties are studied. Further, the GPVs of words lying on surfaces are discussed. The concepts of surface language, language surface and their properties are also studied in this paper.