Geodesic
The gap structure of a family of integer subsets
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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In this paper we investigate the gap structure of a certain family of subsets of $\mathbb{N}$ which produces counterexamples both to the "density version" and the "canonical version" of Brown's lemma. This family includes the members of all complementing pairs of $\mathbb{N}$. We will also relate the asymptotical gap structure of subsets of $\mathbb{N}$ with their density and investigate the asymptotical gap structure of monochromatic and rainbow sets with respect to arbitrary infinite colorings of $\mathbb{N}$.
DOI : 10.37236/3809
Classification : 11B25, 05D10
Mots-clés : piecewise syndetic, complementing pairs, Brown's lemma, Ramsey theory 
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     author = {Andr\'e Bernardino and Rui Pacheco and Manuel Silva},
     title = {The gap structure of a family of integer subsets},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {1},
     doi = {10.37236/3809},
     zbl = {1331.11006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3809/}
}
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André Bernardino; Rui Pacheco; Manuel Silva. The gap structure of a family of integer subsets. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3809

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