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thesis.pdf (1.04 MB)
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Abstract Header
Partition regular polynomial patterns in commutative semigroups
Author Info
Moreira, Joel, Moreira
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194
Abstract Details
Year and Degree
2016, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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.
Committee
Vitaly Bergelson (Advisor)
Pages
139 p.
Subject Headings
Mathematics
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Citations
Moreira, Moreira, J. (2016).
Partition regular polynomial patterns in commutative semigroups
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194
APA Style (7th edition)
Moreira, Moreira, Joel.
Partition regular polynomial patterns in commutative semigroups.
2016. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194.
MLA Style (8th edition)
Moreira, Moreira, Joel. "Partition regular polynomial patterns in commutative semigroups." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194
Chicago Manual of Style (17th edition)
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Document number:
osu1467131194
Download Count:
911
Copyright Info
© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.