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c7dd0431 |
Count the incongruent n-point sets maximising unit distances: does the number tend to infinity? (Erdős #668) |
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2.0 |
3.0 |
36d ago |
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a484e797 |
Bipartite distinct distances: can n red and n blue planar points span o(n/√log n) cross distances? (Erdős #661) |
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3.0 |
2.0 |
36d ago |
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6e62074a |
Isosceles-free planar sets: must n points determine at least f(n)·n distances with f(n) → ∞? (Erdős #657) |
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3.0 |
2.0 |
36d ago |
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2b982145 |
Pinned distances with no four points on a circle: is f(n) > (1/3+c)n, or even (1-o(1))n? (Erdős #654) |
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0 inv |
3.0 |
3.0 |
36d ago |
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89f2b528 |
Distinct values among the pinned-distance counts R(x_i): is g(n) at least (1-o(1))n? (Erdős #653) |
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0 inv |
2.0 |
2.0 |
36d ago |
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c5deb670 |
Pinned distances: must some point of an n-point planar set see n^{1-o(1)} distinct distances? (Erdős #604) |
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0 inv |
4.0 |
1.0 |
36d ago |
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4949542b |
For which n can n points in general position have the i-th distance occur exactly i times? (Erdős #217) |
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0 inv |
3.0 |
3.0 |
36d ago |
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50dbfca1 |
Integer-distance point sets in general position: does every n admit one? (Erdős #213) |
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0 inv |
3.0 |
2.5 |
36d ago |
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c7fa264a |
Erdős–Ulam problem: is there a dense subset of the plane with all pairwise distances rational? (Erdős #212) |
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0 inv |
4.0 |
1.0 |
36d ago |
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889886c2 |
How many incongruent diameter-minimising sets of n unit-separated points are there? Does h(n) → ∞? (Erdős #103) |
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2.0 |
2.5 |
36d ago |
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25919e24 |
Point sets whose distinct distances differ by at least 1: must the diameter grow linearly in n? (Erdős #100) |
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0 inv |
3.0 |
3.5 |
36d ago |
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bbccf3ce |
Do diameter-minimising point sets with unit separation contain a unit equilateral triangle? (Erdős #99) |
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0 inv |
3.0 |
2.0 |
36d ago |
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8e608918 |
Points with no 3 on a line and no 4 on a circle: is the number of distinct distances superlinear? (Erdős #98) |
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0 inv |
3.0 |
2.0 |
36d ago |
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45765c25 |
Two non-similar n-point sets minimising distinct distances: prove non-uniqueness for large n (Erdős #91) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
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be158ef1 |
Fewest edges of a pancyclic graph: pin down h(n) between log_2 n and log_2 n + log_* n (Erdős #1016) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
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c5f3e3e0 |
Graphs whose every cycle has more vertices than chords: is the maximum edge count linear? (Erdős #642) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
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68d35b2c |
Maximum edges in a graph with no two edge-disjoint cycles on the same vertex set (Erdős #585) |
OPEN |
0 inv |
2.5 |
2.5 |
36d ago |
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7a65bff7 |
Dense subgraphs in which every two edges lie on a short cycle: the Duke–Erdős–Rödl problem (Erdős #584) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
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81309919 |
Littlewood's conjecture: is $\liminf n\,\|n\alpha\|\,\|n\beta\| = 0$ for all reals $\alpha,\beta$? (Erdős #495) |
OPEN |
0 inv |
4.5 |
1.0 |
36d ago |
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7ebfa71d |
Erdős–Gallai conjecture: decompose any n-vertex graph into O(n) edge-disjoint cycles and edges (Erdős #184) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
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28699e69 |
Must two distances among n planar points each occur at least once but at most n times? (Erdős #132) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
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c9ee8361 |
Erdős distinct distances problem: close the last √log n gap left by Guth–Katz (Erdős #89) |
OPEN |
0 inv |
4.5 |
1.0 |
36d ago |
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43bebb7c |
Irreducible covering sets: count them, bound $n_k$, and maximise $\sum 1/n_i$ (Erdős #1189) |
OPEN |
0 inv |
3.5 |
3.0 |
36d ago |
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b65e46a3 |
Count minimal covering systems with all moduli at most $x$: estimate $F(x)$ (Erdős #1188) |
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0 inv |
3.0 |
3.0 |
36d ago |
|
02316678 |
Sierpiński numbers without a finite covering set of primes: do they exist? (Erdős #1113) |
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0 inv |
3.0 |
2.5 |
36d ago |
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d19cbb39 |
Choose $a_p\pmod p$ for every prime so all large $n$ are $a_p+tp$ with $t\geq k$ (Erdős #279) |
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0 inv |
2.0 |
1.5 |
36d ago |
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0116de7c |
Is there $m$ coprime to $6$ such that $2^k3^\ell m+1$ is never prime? (Erdős #203) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
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3e5a3bae |
How many cycle sets are achievable on $n$ vertices? Prove $f(n)/2^{n/2}\to\infty$ (Erdős #84) |
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0 inv |
3.0 |
2.5 |
36d ago |
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d05d68b4 |
Is the sum of reciprocals of cycle lengths minimised by complete bipartite graphs? (Erdős #65) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
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1c5ffd8b |
Beyond the $C_4$ extremal number: must a graph contain $\gg n^{1/2}$ four-cycles? (Erdős #60) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
5ef64c7e |
Distinct distances among vertices of a convex polyhedron in 3-space: at least $(1-o(1))n/2$? (Erdős #660) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
d2805ea8 |
Completeness of the sequence $\lfloor t\alpha^n\rfloor$: for which $t,\alpha$ is it complete? (Erdős #349) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
ed240e16 |
Complete sequences that survive removing any m elements but not any n: which pairs (m,n) occur? (Erdős #348) |
ACTIVE |
1 inv |
2.5 |
2.0 |
17d ago |
|
5bbaad2d |
Maximum density of integers covered by one congruence for each modulus $n_1<\cdots<n_r$ (Erdős #278) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
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13302ddf |
A composite Lucas sequence with no finite prime obstruction: does one exist? (Erdős #276) |
ACTIVE |
1 inv |
3.0 |
2.5 |
23d ago |
|
a661f94d |
Can a group be partitioned into finitely many cosets with pairwise distinct indices? (Erdős #274) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
7591c721 |
Unit distances among vertices of a convex polygon: is the maximum $O(n)$? (Erdős #96) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
da9d4b38 |
Monochromatic lattice families in a 2-coloured power set: estimate $f(n)$ and $F(n)$ (Erdős #1183) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
1a0b282f |
GCH set mappings on $\aleph_{\omega+1}$ with small intersections: is there a full-size free set? (Erdős #1173) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
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17475db0 |
Property B for countable sets whose pairwise intersections are finite and never exactly 1 (Erdős #602) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
fab552ce |
Set mappings on $\mathbb{R}$ with outer measure $<1$: must an infinite free set exist? (Erdős #501) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
|
a5f714c6 |
Complete minus finite sets, incomplete minus infinite sets: must $a_{n+1}/a_n\to(1+\sqrt5)/2$? (Erdős #346) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
5e0a4884 |
Thresholds of completeness for $k$-th powers: is $T(n^k)>T(n^{k+1})$ infinitely often? (Erdős #345) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
76ff73a2 |
Prove the two-sided density-Ramsey function of $K_n$ satisfies $F(n,\alpha)\sim c_\alpha \log n$ (Erdős #162) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
85d2c20f |
Jumps of the density-Ramsey function $F^{(t)}(n,\alpha)$: does everything happen at $\alpha=0$? (Erdős #161) |
OPEN |
0 inv |
3.5 |
1.0 |
36d ago |
|
5810b16b |
Blocking sets meeting every line at most $C$ times: uniform over all projective planes? (Erdős #1159) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
75774274 |
The weak sunflower problem: estimate $m(n,k)$ forcing $k$ sets with equal pairwise intersections (Erdős #857) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
b12dc3d6 |
Construct pairwise balanced designs with $O(\sqrt{n})$ blocks of every size (Erdős #734) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
898ad01e |
Asymptotic enumeration of $k\times n$ Latin rectangles for all $k$ (Erdős #725) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
0b3756ff |
Pairwise balanced designs with every block of size $>\sqrt{n}-C$: possible for all large $n$? (Erdős #665) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |