# Questions tagged [erdos]

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28
questions

**2**

votes

**1**answer

103 views

### Probabilistic bound to the number of edge disjoint triangles in a random graph

Let $G$ be a random graph with $n$ vertices, and let $\delta(G)$ be the maximum number of triangles in $G$.
Question. How to prove the bound $$P(\delta(G)) \leq m - t \sqrt{f(m)}) \leq 2e^{-t^2 / 4}$...

**1**

vote

**0**answers

31 views

### Selection theorems and homeomorphism groups

All spaces are separable metrizable.
Let $f:X\to Y$ be a continuous open mapping from a Polish space $X$ onto a zero-dimensional space $Y$. By the Michael selection theorem (zero-dimensional version), ...

**5**

votes

**2**answers

276 views

### Updates on a least prime factor conjecture by Erdos

In the 1993 article "Estimates of the Least Prime Factor of a Binomial Coefficient," Erdos et al. conjectured that
$$\operatorname{lpf} {N \choose k} \leq \max(N/k,13)$$
With finitely many ...

**0**

votes

**1**answer

166 views

### Generalized Erdős multiplication table problem

Consider multiplication operation $$f(x_1,\dots, x_k)=\prod_{i=1}^kx_i$$ where $x_i\in\{1,\dots, n_i\}$ with $n_1,\dots, n_k\in\{1,\dots,\infty\}$.
What is the cardinality of the range?
At $k =2$ ...

**4**

votes

**0**answers

414 views

### The "core" of complete Erdős space

This question is about the Erdős spaces:
$\mathfrak E=\{x\in \ell^2:x_n\in \mathbb Q\text{ for all $n<\omega$}\}$; and
$\mathfrak E_c=\{x\in \ell^2:x_n\in \mathbb P\text{ for all $n<\omega$}\}...

**12**

votes

**2**answers

497 views

### A reformulation of Erdős conjecture on arithmetic progressions

Erdős conjecture on arithmetic progressions states that if $S$ is a set of positive integers such that $c(S):=\sum_{n \in S} \frac{1}{n} = \infty$ (large set), then $ \forall \ell \ge 3$ the set $S$ ...

**5**

votes

**1**answer

363 views

### Countable version of Erdös-Lovasz-Faber conjecture

Let $X$ be an infinite set, and let $(A_n)_{n\in\omega}$ be a collection of subsets of $X$ with the following properties:
$|A_m\cap A_n| \leq 1$ for $m\neq n\in \omega$, and
$|A_n|=\aleph_0$ for all $...

**36**

votes

**2**answers

4k views

### How to find Erdős' treasure trove?

The renowned mathematician, Paul Erdős, has published more than 1500 papers in various branches of mathematics including discrete mathematics, graph theory, number theory, mathematical analysis, ...

**16**

votes

**2**answers

1k views

### Is there any published summary of Erdos's published problems in the American Mathematical Monthly journal?

As we know Erdos has proposed a considerable number of problems in the "American Mathematical Monthly" journal. Is there any published summary of Erdos's published problems in the American ...

**0**

votes

**1**answer

508 views

### Random graphs- Erdos and Renyi 1959 paper

Please refer to this link. It is Erdos and Renyi's first paper on Random Graphs (1959). I am trying to work through it.
I'm struggling with equations (16), (17) and (21).
(16)
I'm not sure why ...

**12**

votes

**0**answers

372 views

### On a relaxed form of Goldbach's conjecture proposed by Erdős

The Goldbach's conjecture says that:
"Every even integer greater that $2$ is the sum of two prime numbers".
Let $\varphi$ denote the Euler's totient function. I remember that a long time ago I read ...

**2**

votes

**0**answers

137 views

### mixing time of random walks on dense Erdos Renyi graphs

Is there anything known about the mixing time of a simple random walk on an Erdos-Renyi graph with parameter $\langle n,d \rangle$ where $d=n^a (0<a<1 )$. I know about Reed et al and Benjamini ...

**2**

votes

**1**answer

443 views

### When an Erdos-Renyi graph is locally tree like?

I would like to know when an ER graph is locally treeing like. In this post.
I found this comment:
I think $N$ is $\log2|V|$, or something like that, in that paper.
They consider binary vectors ...

**1**

vote

**1**answer

233 views

### estimating binomial coefficients

There is a beautiful paper on the arXiv by Andrew Suk containing an asymptotic result about the Erdös-Szekeres convex polygon problem. I am struggling with one of the estimates he makes on page 4. He ...

**15**

votes

**2**answers

2k views

### Many representations as a sum of three squares

Let $r_3(n) = \left|\{(a,b,c)\in {\mathbb Z}^3 :\, a^2+b^2+c^2=n \}\right|$. I am looking for the maximum asymptotic size of $r_3(n)$. That is, the maximum number of representations that a number can ...

**13**

votes

**1**answer

3k views

### What is the source of this E̶r̶d̶ő̶s̶ quote?

Namely, the following one
"All problems appeared once in the [American Mathematical] Monthly."
I remember reading it several years ago... When I first posed the question, I believed that I had ...

**30**

votes

**2**answers

3k views

### The Erdős-Turán conjecture or the Erdős' conjecture?

This has been bothering me for a while, and I can't seem to find any definitive answer. The following conjecture is well known in additive combinatorics:
Conjecture: If $A\subset \mathbb{N}$ and ...

**2**

votes

**3**answers

575 views

### A limit from an Erdos paper

Hi,
I need help to prove that, for $ N = \big\lfloor \frac{1}{2}n\log(n)+cn \big\rfloor $ with $c \in \mathbb R $ and $0 \leq k \leq n: $
$$ \lim_{n\rightarrow +\infty} \dbinom{n}{k} \frac{\dbinom{\...

**3**

votes

**0**answers

672 views

### Paul Erdős and Ramanujan Primes

It's easy to find Ramanujan's proof of Ramanujan primes:
Ramanujan's Proof
Wikipedia mentions that Paul Erdős also had a proof:
Wikipedia article on Bertrand's Postulate
Does anyone know the ...

**3**

votes

**1**answer

484 views

### A question about the number of intersections of lines in $R^{3}$

Suppose I have n lines in $R^{3}$ with the conditions that: no 3 lines in one plane, no 3 lines intersect at one point, for fixed 2 lines, no 3 lines intersect these 2 lines at the same time.
what is ...

**4**

votes

**1**answer

441 views

### Degree reduction argument in Guth-Katz'sproof of Erdos distinct distance problem in the plane

In the middle of page 9 of
http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf.
They said " Now we select a random subset....choosing lines independently with
probability $\frac{Q}{100}$. With ...

**15**

votes

**3**answers

2k views

### Erdos distance problem n=12

The recent paper On the Erdos distinct distance problem in the plane
Authors: Larry Guth, Nets Hawk Katz prodded me to get a non-trivial example. Here is what I cannot find: an example of 12 ...

**2**

votes

**2**answers

335 views

### Determining the vector space for application of Cauchy Schwarz

In the paper "On the Erdős distinct distance problem in the plane" by Larry Guth and Nets Hawk Katz,
http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf
they define the functions $d(P)$, (...

**12**

votes

**2**answers

863 views

### Did Erdős publish his proof of the multiplicative version of the Erdős-Turán conjecture?

I read in an article of Erdős ("Extremal problems in number theory") that he had a proof of the multiplicative version of the Erdős-Turán conjecture. The statement of this theorem is
Let $a_1 < ...

**37**

votes

**4**answers

2k views

### Does there exist a comprehensive compilation of Erdos's open problems?

Fan Chung and Ron Graham's book Erdos on Graphs: His Legacy of Unsolved Problems (A. K. Peters, 1998) collects together all of Erdos's open problems in graph theory that they could find into a single ...

**3**

votes

**1**answer

780 views

### A limit involving the totient function

P. Erdős and Leon Alaoglu proved in [1] that for every $\epsilon > 0$ the inequality $\phi(\sigma(n)) < \epsilon \cdot n$ holds for every $n \in \mathbb{N}$, except for a set of density $0$.
C. ...

**14**

votes

**6**answers

4k views

### If Erdős is published as Erdös in a paper, which do I cite?

There seems to be a few papers around with Erdős written as Erdös. For example:
MR0987571 (90h:11090) Alladi, K.; Erdös, P.; Vaaler, J. D. Multiplicative functions and small divisors. II. J. Number ...

**26**

votes

**5**answers

8k views

### Erdos Conjecture on arithmetic progressions

Introduction:
Let A be a subset of the naturals such that $\sum_{n\in A}\frac{1}{n}=\infty$. The Erdos Conjecture states that A must have arithmetic progressions of arbitrary length.
Question:
I ...