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Partition regular polynomial patterns in commutative semigroups
Moreira, Joel, Moreira

2016, Doctor of Philosophy, Ohio State University, Mathematics.
In 1933 Rado characterized all systems of linear equations with rational coefficients which have a monochromatic solution whenever one finitely colors the natural numbers.
A natural follow-up problem concerns the extension of Rado's theory to systems of polynomial equations.
While this problem is still wide open, significant advances were made in the last two decades.
We present some new results in this direction, and study related questions for general commutative semigroups.

Among other things, we obtain extensions of a classical theorem of Deuber to the polynomial setting and prove that any finite coloring of the natural numbers contains a monochromatic triple of the form {x,x+y,xy}, settling an open problem.

We employ methods from ergodic theory, topological dynamics and topological algebra.
Vitaly Bergelson (Advisor)
139 p.

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Moreira, J. (2016). Partition regular polynomial patterns in commutative semigroups. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Moreira, Joel. "Partition regular polynomial patterns in commutative semigroups." Electronic Thesis or Dissertation. Ohio State University, 2016. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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Moreira, Joel "Partition regular polynomial patterns in commutative semigroups." Electronic Thesis or Dissertation. Ohio State University, 2016. https://etd.ohiolink.edu/

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