Geodesic
Universally image partition regularity
The electronic journal of combinatorics, Tome 15 (2008)
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Many of the classical results of Ramsey Theory, for example Schur's Theorem, van der Waerden's Theorem, Finite Sums Theorem, are naturally stated in terms of image partition regularity of matrices. Many characterizations are known of image partition regularity over ${\Bbb N}$ and other subsemigroups of $({\Bbb R},+)$. In this paper we introduce a new notion which we call universally image partition regular matrices, which are in fact image partition regular over all semigroups and everywhere. We also prove that such matrices exist in abundance.
DOI : 10.37236/865
Classification : 05D10, 54D35, 22A15, 54D80
Mots-clés : partition regularity, image partition regularity, subsemigroups 
@article{10_37236_865,
     author = {Dibyendu De and Ram Krishna Paul},
     title = {Universally image partition regularity},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/865},
     zbl = {1159.05323},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/865/}
}
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Dibyendu De; Ram Krishna Paul. Universally image partition regularity. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/865

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