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Tagged with sumsets inequalities
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Sumsets and a bound
Let $q$ be a positive integer. Is it true there exists a constant $C_q$ such that the following inequality holds for any finite set $A$ of reals:
$$\displaystyle |A+qA|\ge (q+1)|A|-C_q\qquad (1)$$
I ...
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A sumset inequality
A friend asked me the following problem:
Is it true that for every $X\subset A\subset \mathbb{Z}$, where $A$ is finite and $X$ is non-empty, that $$\frac{|A+X|}{|X|}\geq \frac{|A+A|}{|A|}?$$
Here ...
- 11.2k
1
vote
3
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how to proof this Stirling related equation
here is what I need to proof, have no idea were to start. I know there is some connection with the Stirling theorem.
$$
\sum_{i=0}^{d}\binom{m}{i} \leq \left ( \frac{em}{d} \right )^{d}
$$
I tried ...
- 11