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Informally, data mining is derivation of patterns from data. The mathematical mechanics of association mining (AM) is carefully examined from this point. The data is table of symbols, and a pattern is any algebraic/logic expressions derived from this table that have high supports. Based on this view, we have the following theorem: A pattern (generalized associations) of a relational table can be found by solving a finite set of linear inequalities within a polynomial time of the table size. The main results are derived from few key notions that observed previously: (1) Isomorphism: Isomorphic relations have isomorphic patterns. (2) Canonical Representations: In each isomorphic class, there is a unique bitmap based model, called granular data model

Mathematical Foundation of Association Rules - Mining Associations by Solving Integral Linear Inequalities