Effective Results on the Size and Structure of Sumsets
Effective Results on the Size and Structure of Sumsets
Abstract Let $$A \subset {\mathbb {Z}}^d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:mrow> </mml:math> be a finite set. It is known that NA has a particular size ( $$\vert NA\vert = P_A(N)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>N</mml:mi> <mml:mi>A</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>A</mml:mi> …