On a solvable symmetric and a cyclic system of partial difference equations

Abstract

It is shown that the following symmetric system of partial difference equations (Formula presented) is solvable on the combinatorial domain C = {(m, n) ε N 20 : 0 ≤ n ≤ m} \ {(0,0)}, by presenting some formulas for the general solution to the system on the domain in terms of the boundary values c j,j , c j,0 d j,j , d j,0 , j ε N. and the indices m and n. The corresponding result for a related three-dimensional cyclic system of partial difference equations is also proved. These results can serve as a motivation for further studies of the solvability of symmetric, close-to-symmetric, cyclic, close-to-cyclic and other related systems of partial difference equations.