2- AND 3-WAY ON A GRAPH-LATTICE AND COMBINATORIAL IDENTITIES
Graph-lattice has vertices at the points of a plane with a non-negative integer coordinates. Each vertex has two oriented arcs: horizontal and vertical arcs to the neighboring vertices (right and top). The transition probability for each of the arc is equal to. We considered the problem of random walks on the vertices of the graph with restrictions on the achievability. Valid for consideration are only 2(3)-paths. Under the 2(3)-path on the graph-lattice we mean a path of satisfying the next condition - maximum by embedding beginning sub-path consisting only of vertical arcs and all maximum by embedding internal sub-paths consisting only of vertical arcs have a length multiple of 2 (3). We obtain a formula for the number of paths connecting specified vertices of the graph-lattice, found the probability of getting from one vertex to another via 2(3)-paths. The consequence of the latter is the combinatorial identity, which contained elements of Pascal's triangle.