# Questions tagged [sumsets]

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### Different sum combinations of $L$ identical lists of consecutive natural numbers

Given $L$ variables $k_i$ where each $k_{i} \in \{1, 2, 3, \ldots, N\}$ I want to obtain how many different sums $k_{1}+k_{2}+\cdots+k_{L}$ are generated and the value of these sums. There are $L^N$ ...
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### Sumsets with the property "$A+B=C$ implies $A=C-B$"

Let $(G,+)$ be an abelian group and $A$, $B$ and $C$ be finite subsets of $G$ with $A+B=C$. One may conclude that $A\subset C-B$. However, $A$ need not be equal to $C-B$. What is a necessary and ...
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### Existence of m infinite subsets in an arbitrary group such that all products of one element from each (in order) are distinct

Is it true that for every infinite group $G$ and every $m\in\mathbb{N}$ there are infinite subsets $A_0,\dots,A_{m-1}$ such that all the products $a_0\cdot\dots\cdot a_{m-1}$ with $a_i\in A_i$ are ...
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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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### Restricted sumsets - the origins?

The sumset of the subsets $A$ and $B$ of an additively written group is defined by $A+B:=\{a+b\colon a\in A,\ b\in B\}$. The basic idea to add sets has been around since Cauchy at least. Erdős and ...
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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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1 vote
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### Generating Subsets of a Multiset in Ascending Order of the Sums of the Elements of the Subset

I am trying to come up with an algorithm where you can generate combination from a set in a order such that their sums are in increasing order. This set has to be a multiset i.e. repetition allowed. ...
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### Minkowski sum of polytopes from their facet normals and volumes

By Minkowski's work in the early 1900s, every polytope $P\subset\mathbb R^n$ is determined up to translation by its unit facet normals $u_1,\dots,u_k$ and facet volumes $\alpha_1,\dots,\alpha_k$. ...
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### Bounding the size of certain sumsets in the plane

Let $A$ be a finite set in $\mathbb{R}^2$ of $k^2$ elements and consider a set $B=\{x_1,x_2,x_3,x_4\}$ such that the points in $B$ are in general position (no three points on a line). Question 1: Is ...
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### Decomposing a finite group as a product of subsets

My friend Wim van Dam asked me the following question: For every finite group $G$, does there exist a subset $S\subset G$ such that $\left|S\right| = O(\sqrt{\left|G\right|})$ and $S\times S = G$? ...
### The set of lengths of $nX$ gets larger and larger for every non-zero, non-empty, finite $X \subseteq \mathbf N$ with $0 \in X$
Let $H$ be a multiplicatively written monoid with identity $1_H$. Given $x \in H$, we take ${\sf L}_H(x) := \{0\}$ if $x = 1_H$; otherwise, ${\sf L}_H(x)$ is the set of all $k \in \mathbf N^+$ for ...
Let $\mathbb{F}_p$ be a finite field, $A=\{a_1,\dots,a_k\}\subset\mathbb{F}_p^*$ a $k$-element set, for $k<p$. $\mathfrak{S}_k=$permutation gp. Question. Is it true there is always a \$\pi\in\...