Questions tagged [sumsets]
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108 questions
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Bounds on these numbers
Let $[n]$ be the set of natural numbers $1,2,3 \cdots n$ and $k$ be a natural number. Define $S(n,k) = \# \{ A \subset [n] \mid \displaystyle\sum_{i \in A} i =k \}$. My question is; Are there any ...
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How large must "weak Besicovitch" subsets of groups be?
Consider a group $G$; let call $A\subset G$ a weak Besicovitch subset whenever every element of $G$ can be written under the form $gh^{-1}$, where $g,h\in A$.
General question: how large must a weak ...
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An exercise about sum-product estimate
I am struggling with 1.11 exercise from the George Shakan "Discrete Fourier Transform".
Let $A \subset \mathbb{Z}/q\mathbb{Z}$ be any set not containing zero with $|A|>\sqrt2q^{5/8}$. ...
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Additive energy and uniquely representable elements
Suppose that $A$ is a finite, nonempty set in an abelian group. If there is a group element with a unique representation as $a-b$ with $a,b\in A$, then none of $A-A$ and $2A$ are small:
$$ \min\{|A-A|,...
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General asymptotic result in additive combinatorics (sums of sets)
Let $S_1,\cdots,S_k$ be $k$ infinite sets of positive integers. Let $N_i(z)$ be the numbers of elements in $S_i$ that are less or equal to $z$. Let us further assume that
$$N_i(S) \sim \frac{a_i z^{...
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Rewriting a set of integers to get rid of repetition but keeping subset sum ordering
Say, I have a set of 6 +ve integers sorted in ascending order:
$A = \{2,4,4,4,5,7\}$
Now to make it easier to deal with (Minimum one starts with 1) I deducted one from all of them:
$\therefore B= ...
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Is there another representation for the summation: $\sum_{j=1}^{N}\frac{a_j}{(c+a_j)(c+a_j+1)} $, how to reformulate that to keep $c$ out of the sum [closed]
Is there a closed form (without summation) for the summation or at least can I reformulate that so I keep $c$ out of the summation, for example, $c \sum_{n=1}^{N} f(a_n,b_n)$.
$$
\sum_{n=1}^{N}\frac{...
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Prove or disprove this integral of a function, defined on a countable set with infinite limit points, converges to zero [closed]
Edit: I got rid of my old definitions. Everything should be clear now
Since no one has answered my question on MSE, I’m hoping to get an answer here. I apologize if you dislike my writing. I am an ...
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