Number operators in a general quon algebra

The existence of the number operators N_k in a general quon algebra is proved and a general construction of N_k is presented. A new general simple structure of N_k is proved when mod q_ij mod <1, For all i, j in S. General recurrent relations for the corresponding coefficients are constructed and solved in special cases. These solutions are discussed and a conjecture for a general solution is proposed. Cases in which some or all mod q_ij mod =1 are discussed.