34 votes

How to find Erdős' treasure trove?

Paul Erdős's notes on Egyptian fractions are with Ronald Graham, who has reproduced some of them in Paul Erdős and Egyptian Fractions. Graham mentions one unfinished manuscript in which "it is shown ...
Carlo Beenakker's user avatar
17 votes

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

I do not know of such a summary. But JSTOR has spent considerable time indexing the Monthly, including the "Problems and Solutions" sections. So if your library has a JSTOR subscription you can ...
Gerald Edgar's user avatar
  • 40.2k
9 votes

A reformulation of Erdős conjecture on arithmetic progressions

This question is basically asking how good greedy-type constructions of sets without long arithmetic progressions can be. The answer is actually pretty terrible. Firstly, as you note, if $f_k(n)$ is ...
Thomas Bloom's user avatar
  • 6,608
8 votes
Accepted

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

Recently, Thomas Bloom created a website dedicated exactly to this: https://www.erdosproblems.com/ It currently lists 214 problems, both open and closed. They are all tagged and some problems carry ...
Ofir Gorodetsky's user avatar
8 votes

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

For graph theory problems, I find this the most comprehensive resource: http://www.math.ucsd.edu/~erdosproblems/
Dominic van der Zypen's user avatar
8 votes
Accepted

Updates on a least prime factor conjecture by Erdos

The authors of the paper you mention, Erdos, Lacampagne, and Selfridge, define $p(m)$ to be the least prime divisor of $m$ and concern themselves what can be said about $p(\binom{n}{k}).$ I suspect ...
Aaron Meyerowitz's user avatar
7 votes
Accepted

Countable version of Erdös-Lovasz-Faber conjecture

If I understand it correctly, it's false. Let $x \notin A_0 = \{1,2,\dots \}$. Then let $A_i$ all meet at $x$, and also each meet $A$ at $i$ (add extra elements as necessary; they should be irrelevant)...
user44191's user avatar
  • 4,961
7 votes
Accepted

Random graphs- Erdos and Renyi 1959 paper

(16) They split the sum in (13) for $M<s\leq \frac n 2$ and $\frac n 2 < s < n- \frac {2 N_c} n$. In the first case they use (14) and, since the terms are positive, they enlarge the sum to $M&...
Luca Ghidelli's user avatar
5 votes

Erdos distance problem n=12

Thought it might be nice to show the set placed on the hexagonal lattice. Here’s a Desmos link if you wish to play around with such point configurations.
Alon Amit's user avatar
  • 6,414
4 votes
Accepted

estimating binomial coefficients

We have $$\binom{x}k=\frac{x(x-1)\dots (x-k+1)}{k!}\leqslant \frac{x^k}{k!}\leqslant x^k$$ for positive integers $x, k$. Applying this to $k=[2n^{3/4}]-2$, $x=n+k-2\leqslant 2n$ (for large $n$) we get ...
Fedor Petrov's user avatar
4 votes

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

I do not think that anyone ever made an effort to collect ALL problems of Erdos. In the later part of his life he liked to give talks on various conferences under the title "My favorite unsolved ...
Alexandre Eremenko's user avatar
4 votes
Accepted

Generalized Erdős multiplication table problem

This problem is solved for $k\leq 5$ and open for $k\geq 6$. See Koukoulopoulos's paper for more details.
GH from MO's user avatar
  • 98.2k
3 votes

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

There is a (lovely) corollary of Talagrand's inequality contained in Alon and Spencer's Probabilistic Method which gives it immediately. Here's a version of it: Definition: Let $f: N \to N$ be a ...
Marcus M's user avatar
  • 900
3 votes

Updates on a least prime factor conjecture by Erdos

The conjecture as written is false: Let $N=194+(2*3*5*7*11*13)*2n$, $k=N-2$, where $n$ is a natural number. Then $C(N,k)=C(N,2)=(97+2*3*5*7*11*13*n)(193+2*3*5*7*11*13*2n)$, having no prime factors $\...
LeechLattice's user avatar
  • 9,421
2 votes

A reformulation of Erdős conjecture on arithmetic progressions

I asked Prof. Jaroslaw Wróblewski by email, below is his answer (reproduced with his authorization): I do not know of any new results regarding searching a set $B$ in $\mathcal{A}_3$ [the set of ...
Sebastien Palcoux's user avatar
1 vote

When an Erdos-Renyi graph is locally tree like?

it has to do with the clustering coefficient. See the bottom of page 5 here: https://aaronclauset.github.io/courses/3352/csci3352_2021_L3.pdf
user7400474's user avatar

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