On cyclic 〈m,n〉-enumerations Original Research Article

A word is called cyclic if each letter occurs in it an even number of times. A cyclic word X on the n-letter alphabet is called a cyclic 〈m,n〉-word if there is a letter in each subword of X occurring in it an odd number of times, and in each subword of X of length m all the letters are distinct. Such words induce 〈m,n〉-enumerations of binary strings (Methods of Discrete Analysis for Solving Combinatorial, Problems, Vol. 34, Novosibirsk, Russia, 1980, pp. 8). For any positive integers n and m, where m