On difference sets with small $$\lambda $$ λ
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DOI: 10.1007/s10801-020-00992-x
Abstract: In a 1989 paper, Arasu (Arch Math 53:622–624, 1989) used an observation about multipliers to show that no (352, 27, 2) difference set exists in any abelian group. The proof is quite short and required no computer… read more here.
Keywords: small lambda; difference sets; difference; show ... See more keywords
The Typical Structure of Sets With Small Sumset
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DOI: 10.1093/imrn/rnab021
Abstract: In this paper we determine the number and typical structure of sets of integers with bounded doubling. In particular, improving recent results of Green and Morris, and of Mazur, we show that the following holds… read more here.
Keywords: small sumset; lambda; sets small; structure sets ... See more keywords
MULTIDIMENSIONAL VAN DER CORPUT SETS AND SMALL FRACTIONAL PARTS OF POLYNOMIALS
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DOI: 10.1112/s0025579318000529
Abstract: We establish Diophantine inequalities for the fractional parts of generalized polynomials $f$, in particular for sequences $\nu(n)=\lfloor n^c\rfloor+n^k$ with $c>1$ a non-integral real number and $k\in\mathbb{N}$, as well as for $\nu(p)$ where $p$ runs through… read more here.
Keywords: van der; der corput; corput sets; multidimensional van ... See more keywords