Abstract
This chapter presents a general theorem on domination of which the enumeration of paths becomes a special case and study some of its variations and extensions. Also, higher dimensional paths under restrictions are counted. Finally, an important 1:1 correspondence is given between paths with various types of diagonal steps (defined later) and paths without diagonal steps. The chapter presents a continuous analogue of the theorem on domination. Various theorems are proved in the chapter. Higher dimensional paths, and types of diagonal steps and a correspondence are reviewed.
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