Abstract. Given formal differential operators F i on polynomial algebra in several variables x 1 , . . . , x n , we discuss finding expressions K l determined by the equationand their applications. The expressions for K l are related to the coproducts for deformed momenta for the noncommutative space-times of Lie algebra type and also appear in the computations with a class of star products. We find combinatorial recursions and derive formal differential equations for finding K l . We elaborate an example for a Lie algebra su(2), related to a quantum gravity application from the literature.

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We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach. Anyonic-like systems are briefly discussed.