Some New Exact van der Waerden numbers
نویسندگان
چکیده
For positive integers r, k0, k1, ..., kr−1, the van der Waerden number w(k0, k1, ..., kr−1) is the least positive integer n such that whenever {1, 2, . . . , n} is partitioned into r sets S0, S1, ..., Sr−1, there is some i so that Si contains a ki-term arithmetic progression. We find several new exact values of w(k0, k1, ..., kr−1). In addition, for the situation in which only one value of ki differs from 2, we give a precise formula for the van der Waerden function (provided this one value of ki is not too small).
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