Partition regular polynomial patterns in commutative semigroups

Bibliographic Details
Main Author:	Moreira, Joel, Moreira
Language:	English
Published:	The Ohio State University / OhioLINK 2016
Subjects:	Mathematics
Online Access:	http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194

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spelling	ndltd-OhioLink-oai-etd.ohiolink.edu-osu14671311942021-08-03T06:37:07Z Partition regular polynomial patterns in commutative semigroups Moreira, Joel, Moreira 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. 2016-11-22 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194 http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection	NDLTD
language	English
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics Moreira, Joel, Moreira Partition regular polynomial patterns in commutative semigroups
author	Moreira, Joel, Moreira
author_facet	Moreira, Joel, Moreira
author_sort	Moreira, Joel, Moreira
title	Partition regular polynomial patterns in commutative semigroups
title_short	Partition regular polynomial patterns in commutative semigroups
title_full	Partition regular polynomial patterns in commutative semigroups
title_fullStr	Partition regular polynomial patterns in commutative semigroups
title_full_unstemmed	Partition regular polynomial patterns in commutative semigroups
title_sort	partition regular polynomial patterns in commutative semigroups
publisher	The Ohio State University / OhioLINK
publishDate	2016
url	http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194
work_keys_str_mv	AT moreirajoelmoreira partitionregularpolynomialpatternsincommutativesemigroups
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Partition regular polynomial patterns in commutative semigroups

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