  In this paper we bring together the areas of combinatorics and propositional
satisfiability. Many combinatorial theorems establish, often constructively,
the existence of positive integer functions, without actually providing their
closed algebraic form or tight lower and upper bounds. The area of Ramsey
theory is especially rich in such results. Using the problem of computing van
der Waerden numbers as an example, we show that these problems can be
represented by parameterized propositional theories in such a way that
decisions concerning their satisfiability determine the numbers (function) in
question. We show that by using general-purpose complete and local-search
techniques for testing propositional satisfiability, this approach becomes
effective -- competitive with specialized approaches. By following it, we were
able to obtain several new results pertaining to the problem of computing van
der Waerden numbers. We also note that due to their properties, especially
their structural simplicity and computational hardness, propositional theories
that arise in this research can be of use in development, testing and
benchmarking of SAT solvers.
