Questions tagged [sumset]
For questions regarding sumsets such as $A+B$, the set of all sums of one element from $A$ and the other from $B$.
28
questions with no upvoted or accepted answers
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Sidon sets in finite groups
Suppose $G$ is a group, $S \subset G$. Let’s call $S$ a Sidon subset iff $\forall$ quadruples $(a, b, c, d)$ of distinct elements of $S$ we have $ab \neq cd$ (named after Simon Sidon who studied such ...
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Where can I find this article by I. Ruzsa?
Title says it all. Have tried googling and my college library, but no success so far.
I. Ruzsa, On the cardinality of $A + A$ and $A − A$. In Combinatorics (Keszthely, 1976), Coll. Math. Soc. Bolyai ...
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Limit measuring failure of sum-set cancellability
Suppose $A$, $B$ are finite sets of positive integers.
Let $$\mathcal{S}_n = \{C \subset [1,n] \, : \, A+C = B+C \}, $$ and denote $a_n = |\mathcal{S}_n|$.
Note that for any $X \in \mathcal{S}_n$ ...
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Existence of a nilpotent subgroup $N \leq G$ of step $\leq n$ such that a finite $A$ is in $K^{O_n(1)}$ left cosets of $N$
Some extra details left out of the title:
Given a group $G$, a symmetric subset $A \subset G$ containing $1$ is called a $K$-approximate group if $|A^2| = |\{ab \mid a,b \in A\}| \leq K|A|$
We are ...
- 2,683
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1
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682
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What is first edge position in the Minkowski sum of two convex polygons in the plane?
I am trying to understand the informal algorithm of the Minkowski sum of two convex polygons in the plane as described here:
Then I tried to apply this method of the Minkowski sum in the example ...
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Which sets of $n-1$ non-multiples of $n$ can't make a multiple of $n$ using $+,-$?
This is a follow up to my previous question (see linked question).
In short, there it is shown that if $n$ is prime, then any set can make it.
I want to characterize sets $\mathbb A_n$ of multisets $...
- 12.5k
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Lower-bounding the density of 3A in terms of that of 2A
Let $A\subset\mathbb{N}$ and $2A=A+A=\{a+b \lvert a,b\in A\}$ and $3A=2A+A$. I wonder how small the density of $3A$ can be, knowing that the density of $2A$ is, say, $\beta >0$, but not knowing ...
- 21
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$p$ divides $ax+by+cz$
I am going to ask here a generalization of this other question:
Problem Fix $\varepsilon>0$ and let $p$ be a sufficiently large prime. Then, show that, for every $X\subseteq \{1,\ldots,p\}$ with $|...
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A Question on the Brunn-Minkowski inequality
It is a direct consequence of the Brunn-Minkowski inequality that
\begin{equation}
|A\oplus B| - \Big(\sqrt{|A|}+\sqrt{|B|}\Big)^2 \geq |A\oplus\tilde{B}| - \Big(\sqrt{|A|}+\sqrt{|\tilde{B}|}\Big)^...
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Asymptotic behavior of a set of nonnegative integers whose sumset with itself is the nonnegative integers
Let $S$ be a set of nonnegative integers such that the sumset $S+S$ is the nonnegative integers. If it can, what is the fastest growing function $f$ such that the number of elements of $S$ less than $...
- 4,057
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Minkowski sum of disks in 3D
Suppose we have a set of disks in $\Bbb R^3$. These disks are neither parallel nor perpendicular to each other. In general, is it possible to formulate (or write an equation for) the object ...
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1
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A finite Fibonacci sum
Is there a closed form for
$$
A(n)=\sum_{k=1}^n\binom{n}{k}\frac{F_k}k
$$
A closed form that is not in terms of two hypergeometric functions.
- 11
1
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101
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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= ...
- 11
1
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Coset Progression is Freiman Isomorphic to Bohr Set
For an abelian group $G$, $H$ a finite subgroup of $G$, $x_1, \dots, x_r \in G$ and $L_1, \dots, L_r \in \mathbb N$, let:
$P(x ; L) = P(x_1, \dots, x_r ; L_1, \dots, L_r) = \{l_1x_1 + \dots + l_rx_r ...
- 2,683
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Retrieve a series knowing all its convergent infinite powersums
We would like to identify $s_n$ (non-increasing series) once we know, assuming are all of them convergent:
$$S_k=\sum_{n>=0}{s_n^k}$$
Known for all k values.
As example $\zeta(2k)$ should ...
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