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- W2964200527 abstract "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." @default.
- W2964200527 created "2019-07-30" @default.
- W2964200527 creator A5009489875 @default.
- W2964200527 date "2017-08-25" @default.
- W2964200527 modified "2023-09-26" @default.
- W2964200527 title "Multidimensional Lower Density Versions of Plünnecke’s Inequality" @default.
- W2964200527 doi "https://doi.org/10.37236/6221" @default.
- W2964200527 hasPublicationYear "2017" @default.
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