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Mathematics > Combinatorics

arXiv:1408.1088 (math)
[Submitted on 5 Aug 2014 (v1), last revised 10 Nov 2014 (this version, v3)]

Title:Enumeration of monochromatic three term arithmetic progressions in two-colorings of any finite group

Authors:Erik Sjöland
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Abstract:There are many extremely challenging problems about existence of monochromatic arithmetic progressions in colorings of groups. Many theorems hold only for abelian groups as results on non-abelian groups are often much more difficult to obtain. In this research project we do not only determine existence, but study the more general problem of counting them. We formulate the enumeration problem as a problem in real algebraic geometry and then use state of the art computational methods in semidefinite programming and representation theory to derive lower bounds for the number of monochromatic arithmetic progressions in any finite group.
Comments: 17 pages. Update v2: Corrected typos and references. Update v3: Incorporated feedback
Subjects: Combinatorics (math.CO)
Cite as: arXiv:1408.1088 [math.CO]
  (or arXiv:1408.1088v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1408.1088

Submission history

From: Erik Sjöland [view email]
[v1] Tue, 5 Aug 2014 18:34:50 UTC (18 KB)
[v2] Thu, 28 Aug 2014 18:59:37 UTC (18 KB)
[v3] Mon, 10 Nov 2014 18:57:16 UTC (13 KB)
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