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Math Help - Erdos and ramsey theory

  1. #1
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    Erdos and ramsey theory

    So I'm writting a paper on Paul Erdos, but im still early on in my math undergrad. Im trying to find a simple answer as to what Erdos did with Ramsey theory and extremal combinatorics, but i keep coming across tough to understand scientific papers.
    Last edited by gbux512; April 12th 2012 at 07:32 AM.
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  2. #2
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    Re: Erdos and ramsey theory

    So I'm writting a paper on Paul Erdos, but im still early on in my math undergrad. Im trying to find a simple answer as to what Erdos did with Ramsey theory and extremal combinatorics, but i keep coming across tough to understand scientific papers.
    In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem. While Ramsey's theorem makes it easy to prove that every sequence of distinct real numbers contains a monotonically increasing infinite sub sequence or a monotonically decreasing infinite sub sequence, the result proved by Paul Erdős and George Szekeres goes further. For given r, s they showed that any sequence of length at least (r − 1)(s − 1) + 1 contains a monotonically increasing sub sequence of length r or a monotonically decreasing sub sequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending problem.
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