Geodesic
Convolution estimates and number of disjoint partitions
Paata Ivanisvili1
1Kent State University
The electronic journal of combinatorics, Tome 24 (2017) no. 2
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Let $X$ be a finite collection of sets. We count the number of ways a disjoint union of $n-1$ subsets in $X$ is a set in $X$, and estimate the number from above by $|X|^{c(n)}$ where $$c(n)=\left(1-\frac{(n-1)\ln (n-1)}{n\ln n} \right)^{-1}.$$ This extends the recent result of Kane-Tao, corresponding to the case $n=3$ where $c(3)\approx 1.725$, to an arbitrary finite number of disjoint $n-1$ partitions.
DOI : 10.37236/7042
Classification : 11B30
Mots-clés : clusters, disjoint partitions, Hamming cube

Paata Ivanisvili  1

1 Kent State University 
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     author = {Paata Ivanisvili},
     title = {Convolution estimates and number of disjoint partitions},
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Paata Ivanisvili. Convolution estimates and number of disjoint partitions. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/7042

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