Multidimensional lower density versions of Plünnecke's inequality
The electronic journal of combinatorics, Tome 24 (2017) no. 3
We investigate the lower asymptotic density of sumsets in $\mathbb{N}^2$ by proving certain Plünnecke type inequalities for various notions of lower density in $\mathbb{N}^2$. More specifically, we introduce a notion of lower tableaux density in $\mathbb{N}^2$ which involves averaging over convex tableaux-shaped regions in $\mathbb{N}^2$ which contain the origin. This generalizes the well known Plünnecke type inequality for the lower asymptotic density of sumsets in $\mathbb{N}$. We also provide a conjectural Plünnecke inequality for the more basic notion of lower rectangular asymtpotic density in $\mathbb{N}^2$ and prove certain partial results.
DOI :
10.37236/6221
Classification :
11B30, 11B13, 11P70
Mots-clés : additive combinatorics, sumsets, asymptotic density
Mots-clés : additive combinatorics, sumsets, asymptotic density
Affiliations des auteurs :
Kamil Bulinski 1
@article{10_37236_6221,
author = {Kamil Bulinski},
title = {Multidimensional lower density versions of {Pl\"unnecke's} inequality},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/6221},
zbl = {1407.11020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6221/}
}
Kamil Bulinski. Multidimensional lower density versions of Plünnecke's inequality. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6221
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