Partitions and sums of integers with repetition |
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Authors: | Neil Hindman |
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Institution: | Mathematics Department, California State University, Los Angeles 90032 USA |
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Abstract: | A partition of N is called “admissible” provided some cell has arbitrarily long arithmetic progressions of even integers in a fixed increment. The principal result is that the statement “Whenever {Ai}i < r is an admissible partition of N, there are some i < r and some sequence 〈xn〉n < ω of distinct members of N such that xn + xm?Ai whenever {m, n} ? ω″ is true when r = 2 and false when r ? 3. |
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