A DIOPHANTINE CONSTRUCTION OF AN EXACT ALGEBRAIC FORMULA FOR GRADED PARTITION FUNCTIONS

A DIOPHANTINE CONSTRUCTION OF AN EXACT ALGEBRAIC FORMULA FOR GRADED PARTITION FUNCTIONS

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

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