A Variant of the Hales-jewett Theorem
نویسنده
چکیده
It was shown by V. Bergelson that any set B ⊆ N with positive upper multiplicative density contains nicely intertwined arithmetic and geometric progressions: For each k ∈ N there exist a, b, d ∈ N such that ̆ b(a + id) : i, j ∈ {1, 2, . . . , k} ̄ ⊆ B. In particular one cell of each finite partition of N contains such configurations. We prove a Hales-Jewett type extension of this partition theorem.
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تاریخ انتشار 2008