On the quantity of partially stationary functions of ternary logic

Background. Boolean and multi-valued functions are the main research object of discrete mathematics. They represent dependences between values admitting the final value set. There several ways to describe such dependencies, and in practice one often encounters a tabular function set and a set in the form of a polynomial. Both these representations of functions may be expressed as vectors. In case of a tabular function set it is a vector of its values, in case of a polynomial set - a vector of polynomial coefficients. Transformation of a function value vector into a vector of coefficients of its polynomials in the Boolean case is the Mobius transformation. The fixed points of such transformation the author has suggested to call stationary functions. Let $\alpha$ be a vector consisting of n elements of $E_3$ field. $\alpha$-transformation of f function shall be called such $g=v_{\widetilde{\alpha}}(f)$ function that $g(x_1,...,x_n)=f(x_1+\alpha_1,...,x_n+\alpha_n)$. If $v_{\widetilde{\alpha}}(f)=f$, then such function shall be called a partially stationary one relative to $\alpha$ vector. The aim of the study is to find the quantity of partially stationary functions in ternary logic for any $\alpha$ vector. Materials and methods. Finding the quantity of partially stationary functions is based on some features of such functions, obtained in the course of transformation research. It is proved that the quantity of partially stationary functions depends only on the number of zeros, ones and twos in $\alpha$ vector, and doesn't depend on their order in the vector. Conclusion and results. The author found the precise quantity of partially stationary functions, relative to $\alpha$ vector, of ternary logic for any $\alpha$ vector.