Parametrisation of solutions of parametric equation in free monoid
In this paper we introduce recursion functions Fi(x(1),x(2))lambda(1),...,lambda(s) (s greater than or equal to 0), Th(x(1),x(2),x(3))(i)lambda(1),...,lambda(2s) (i = 1,2,3; s greater than or equal to 0), Ro(x(1),x(2),x(3))i mu(1),..., mu(s) (i = 1,2,3; s greater than or equal to 0) of the word variables x(1),x(2),x(3), natural number variables lambda(k) and variables mu(k), whose values are finite sequences of natural number variables. By means of these functions we give expressions for the family of solutions of the parametric equation x(1)x(2)(alpha)x(3)x(4) = x(3)x(1)(beta)x(2)x(5), where x(1),x(2),x(3),x(4),x(5) are word variables, and alpha,beta are natural number variables, in a free monoid. (C) 2000 Published by Elsevier Science B.V. All rights reserved.
equation free monoid general solution