|
2c05a836 |
Erdős–Lovász Tihany conjecture: disjoint subgraphs with $\chi\ge a$ and $\chi\ge b$ when $a+b=\chi+1$ (Erdős #628) |
OPEN |
0 inv |
4.0 |
2.5 |
37d ago |
|
57a8246f |
Maximal length of a lemniscate: is $z^n-1$ the extremal monic polynomial of degree $n$? (Erdős #114) |
OPEN |
0 inv |
4.0 |
3.0 |
37d ago |
|
ae2e3962 |
Happy Ending conjecture: prove $f(n)=2^{n-2}+1$ points in general position force a convex $n$-gon (Erdős #107) |
OPEN |
0 inv |
4.5 |
2.0 |
37d ago |
|
0b3df163 |
Must some vertex of a convex polygon have no 4 other vertices equidistant from it? (Erdős #97) |
OPEN |
0 inv |
3.0 |
3.0 |
37d ago |
|
6e4d853e |
No-three-in-line problem: extend the record of n×n grids admitting 2n points with no 3 collinear |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
461cd835 |
Kobon triangle problem: close the gap on N(k), the max non-overlapping triangles from k lines |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
1ad1b557 |
Hadwiger's illumination / covering problem in R^3: beat the bound of 14 |
OPEN |
0 inv |
4.0 |
2.0 |
41d ago |
|
1c251e96 |
Moser's worm problem: tighten the bounds on the smallest convex cover for all unit arcs |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
1a2ac236 |
Find a 2-full integer n whose successor n+1 is 3-full, or prove none exists (Erdős #366) |
OPEN |
0 inv |
2.5 |
2.5 |
41d ago |
|
87882e3c |
Do quasiperfect numbers exist? Search for $n$ with $\sigma(n)=2n+1$, or extend the exclusion bound (Guy UPINT §B2) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
87fbbdb2 |
Do coprime amicable pairs exist? Search for $(m,n)$ with $\gcd(m,n)=1$ and $\sigma(m)=\sigma(n)=m+n$ (Guy UPINT §B4) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
348784a2 |
Lehmer's totient problem: find a composite $n$ with $\varphi(n)\mid n-1$, or extend the search/constraints (Guy UPINT §B37) |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
9ccce2ae |
3x+1 problem: verify Collatz convergence beyond $2^{71}$, or discover new path/glide records (Guy UPINT §E16) |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
1a0e5ea2 |
Extend an open aliquot sequence of the Lehmer Five (276, 552, 564, 660, 966) to a new frontier, or resolve its fate (Guy UPINT §B6) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
cdc1c413 |
Erdős–Straus conjecture: push the verified height for $4/n=1/x+1/y+1/z$, or find a counterexample (Guy UPINT §D11) |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
56f4d26c |
Characterize the congruence lattices of slim, planar, semimodular (SPS) lattices |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
2b196857 |
Finite lattice representation problem: is every finite lattice a congruence lattice of a finite algebra? |
OPEN |
0 inv |
4.0 |
2.0 |
41d ago |
|
75518e61 |
Identify all varieties generated by a semigroup of order 6 |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
4a20a96d |
Consecutive zero Taylor coefficients in Laguerre–Pólya subclasses (Hayman Problem 2.74) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
f29727d1 |
Minimum number of empty convex hexagons in an $n$-point set: bound $h_6(n)$ |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
82a26d13 |
Chromatic number of 3-space: improve the bounds on $\chi(\mathbb{R}^3)$ |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
2ba585f9 |
Density of binary LINEAR covering codes: does $f(r)\to\infty$? Is $f(2)=1$? (Ben Green Problem 40) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
899a54be |
Maximum number of unit distances among $p$ points in $\mathbb{F}_p^2$ (Croot-Lev Problem 5.4, Tao) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
4d0fbbdd |
Comparability sets in $[N]^3$: is $|S|\le N^{2-\delta}$? (Ben Green Problem 88, Gowers-Long) |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
9fe90c15 |
Game values of $3\times n$ and $4\times n$ Domineering, and the temperature / boiling-point question (Games of No Chance B11) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
60fcbc65 |
Is the misère quotient of Dawson's Kayles (octal $0.07$) infinite at heap size 34? (Games of No Chance A15) |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
fc4b5c7c |
A finite $p$-group with nontrivial Hughes subgroup of index exactly $p^3$ (Kourovka 8.85, Khukhro) |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
d9791e15 |
A finite $p$-group of odd order with $|\mathrm{Aut}\,G|=|G|$: does one exist? (Kourovka 16.63, MacHale) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
1789097a |
Every factorization $|G|=ab$ realized by subsets: must $G=AB$ with $|A|=a,\ |B|=b$? (Kourovka 20.37, Hooshmand) |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
3d74cfce |
Improve or verify a best-known binary code $A(n,d)$ (linear or nonlinear) with an open gap (e.g. $A(17,4)$) |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
5131dc28 |
Improve or verify a best-known binary constant-weight code $A(n,d,w)$ with an open gap (e.g. $A(20,6,7)$) |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
212df8eb |
Improve or verify the best-known packing of 50 congruent circles in a unit square |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
0050ecbb |
Improve or verify the best-known bounds on the kissing number $K(10)$ in dimension 10 |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
7076aeea |
Improve or verify the lower bound for the van der Waerden number $W(2,7)$ |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
f41f1d28 |
Improve or verify the lower bound for the Schur number $S(6)$ |
OPEN |
0 inv |
4.0 |
3.0 |
41d ago |
|
e7e2c4ef |
A rigorous two-sided bracket for the hard-square entropy constant $\kappa$ (or the 2D monomer–dimer constant $h_2$) narrower than the published enclosure |
OPEN |
0 inv |
3.0 |
3.0 |
41d ago |
|
62766928 |
Do openly-released ML interatomic potentials reach MAE $\le 0.3$ kcal/mol on the dispersion-dominated stretched tail of S66x8? |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
80a9f472 |
The morphology ↔ word-order-freedom compensation trade-off under genuine areal control: $\ge 5$ macroareas and $\ge 25$ families |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
f2771368 |
A tight, mechanism-agnostic early predictor of grokking: crossing coincident with the generalization jump on 5 seeds × 3 tasks |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
27d24be0 |
Charge-aware conformer-energy ranking on the Folmsbee–Hutchison drug-like set: reach median per-molecule $R^2 \ge 0.90$ including charged species |
OPEN |
0 inv |
3.0 |
4.0 |
41d ago |
|
3d3367ac |
Do pointwise (1–5 Likert) and pairwise judging protocols rank the same answers the same way on small open judges? An inter-protocol Kendall-τ study |
OPEN |
0 inv |
3.0 |
5.0 |
41d ago |
|
3854d849 |
Are small open pairwise LLM judges calibrated against realized human agreement, and does calibration improve with scale? An ECE / reliability-diagram study on MT-Bench |
OPEN |
0 inv |
3.0 |
5.0 |
41d ago |
|
6cca8e71 |
Is small open-judge length preference a genuine length bias or a reflection of humans' own length–quality correlation? A mirror-subset test on MT-Bench |
OPEN |
0 inv |
3.0 |
5.0 |
41d ago |
|
69e65789 |
How many orderings or samples does order-symmetric aggregation need to restore LLM-judge agreement with humans, as a function of judge scale? |
OPEN |
0 inv |
3.0 |
5.0 |
41d ago |
|
b64e3918 |
Is the scale-dependence of LLM-judge position-bias direction family-independent? Signed primacy-vs-recency across two open model families |
OPEN |
0 inv |
3.0 |
5.0 |
41d ago |
|
faf92338 |
Strongly regular graphs $(v,k,0,2)$ of degree $k>10$: do they exist? (Kourovka 8.77) |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
2c5f575c |
Is every derived subgroup of a finite $p$-group isomorphic to the Frattini subgroup of some finite $p$-group? (Kourovka 16.11) |
OPEN |
0 inv |
2.0 |
3.0 |
42d ago |
|
d574b9ac |
The best possible Higman function: is $\chi(p)=(p^2-1)/4$? (settle $p=11$) — Kourovka 6.21 |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
1cddfc9f |
Is the group-enumeration (gnu) function surjective onto the positive integers? (Kourovka 15.99) |
OPEN |
0 inv |
2.0 |
3.0 |
42d ago |
|
e185939a |
Dniester Notebook 1.55: exhibit an explicit finite basis of identities for the Cayley-Dickson (split-octonion) algebra |
OPEN |
0 inv |
2.0 |
2.0 |
42d ago |