On the number of functions of k -valued logic which are polynomials modulo composite k
Светлана Николаевна Селезнева · Discrete Mathematics and Applications · 2017
Abstract A function of k -valued logic is called polynomial if it may be represented by a polynomial modulo k . For any composite number k we propose a uniquely defined canonical form of polynomials for polynomial functions of k -valued logic depending on an arbitrary number of variables. This canonical form is used to find, for any composite k , a formula for the number of n -place polynomial functions of k -valued logic. As a corollary, for any composite k we find the asymptotic behaviour of the logarithm of the number of n -place polynomial functions of k -valued logic.