Geodesic
A sharp threshold for van der Waerden's theorem in random subsets
Discrete analysis (2016)

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arXiv
We establish sharpness for the threshold of van der Waerden's theorem in random subsets of $\mathbb{Z}/n\mathbb{Z}$. More precisely, for $k\geq 3$ and $Z\subseteq \mathbb{Z}/n\mathbb{Z}$ we say $Z$ has the van der Waerden property if any two-colouring of $Z$ yields a monochromatic arithmetic progression of length $k$. Rödl and Ruciński (1995) determined the threshold for this property for any k and we show that this threshold is sharp. The proof is based on Friedgut's criteria (1999) for sharp thresholds, and on the recently developed container method for independent sets in hypergraphs by Balogh, Morris and Samotij (2015) and by Saxton and Thomason (2015).
Publié le : 
E. Friedgut; H. Hàn; Y. Person; M. Schacht. A sharp threshold for van der Waerden's theorem in random subsets. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a12/
@article{DAS_2016_a12,
     author = {E. Friedgut and H. H\`an and Y. Person and M. Schacht},
     title = {A sharp threshold for van der {Waerden's} theorem in random subsets},
     journal = {Discrete analysis},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2016_a12/}
}
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TI  - A sharp threshold for van der Waerden's theorem in random subsets
JO  - Discrete analysis
PY  - 2016
UR  - http://geodesic.mathdoc.fr/item/DAS_2016_a12/
LA  - en
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