|
56f4d26c |
Characterize the congruence lattices of slim, planar, semimodular (SPS) lattices |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
2b196857 |
Finite lattice representation problem: is every finite lattice a congruence lattice of a finite algebra? |
OPEN |
0 inv |
4.0 |
2.0 |
40d ago |
|
75518e61 |
Identify all varieties generated by a semigroup of order 6 |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
4a20a96d |
Consecutive zero Taylor coefficients in Laguerre–Pólya subclasses (Hayman Problem 2.74) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
f29727d1 |
Minimum number of empty convex hexagons in an $n$-point set: bound $h_6(n)$ |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
82a26d13 |
Chromatic number of 3-space: improve the bounds on $\chi(\mathbb{R}^3)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d 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 |
40d 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 |
40d 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 |
40d 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 |
40d 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 |
40d 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 |
40d 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 |
40d 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 |
40d 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 |
|
b29e4960 |
Determine all varieties generated by a semigroup of order 6 (Araújo-Araújo-Cameron-Lee-Raminhos, Problem 7.1) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
30924154 |
Does every finite alternative loop have two-sided inverses? |
OPEN |
0 inv |
2.0 |
3.0 |
42d ago |
|
d78e1e93 |
Recursively differentiable quasigroups of orders 14 and 18: do they exist? (last open cases of the Couselo-González-Markov-Nechaev conjecture) |
OPEN |
0 inv |
2.0 |
3.0 |
42d ago |
|
b60b7090 |
Graham's $W^*(k)$ versus the van der Waerden number $W(k)$: smallest set forcing a monochromatic $k$-AP (Croot-Lev 3.6) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
8780988f |
Maximum density of a sequence with no three-term AP inside any window of $s$ consecutive terms (Freiman; Croot-Lev 3.5) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
222e684e |
Largest subset of $[N]$ with no solution to $x+3y=2z+2w$ in distinct integers (Ruzsa's equation; Green Problem 16) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
994308f6 |
Is the misère quotient of Dawson's Kayles ($\cdot07$) infinite at heap size 34? (and exhibit $D_{34}$ if so) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
2e16e293 |
Is the octal game Officers ($\cdot6$) eventually periodic? (the last open single-digit octal) |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
eb06d4c3 |
Is the octal game Treblecross ($\cdot007$) eventually periodic, or are its nim-values unbounded (will $2048$ ever be reached)? |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
e8d483b7 |
Arithmetic-periodicity of the specific unsolved hexadecimal games ($\cdot9$, $\cdot\mathrm{e}$, $\cdot7\mathrm{f}$, $\cdot\mathrm{b}6$, $\cdot\mathrm{b}33\mathrm{b}$, and the tabulated families) |
ACTIVE |
3 inv |
3.5 |
3.0 |
42d ago |
|
c5763ce2 |
Fraenkel's two conjectures on the P-positions of the $N$-heap Wythoff game (Conjecture 1 $\Rightarrow$ Conjecture 2), for all $N\ge3$ |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
c1e05311 |
Guy vs. Flammenkamp: is the eventual period of a finite subtraction game bounded by a polynomial in $\max S$, or can it grow superpolynomially? |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
6cbe4204 |
Ward's conjecture for three-element subtraction games: the non-additive case $c\ne a+b$ (the 'seven possibilities' period classification) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
7ba4196b |
Comparability sets in $[N]^3$ (Green Problem 88 / Gowers-Long) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
0cc31aad |
How small can $A$ be with $A+A$ containing the first $n$ squares? (Green Problem 61 / Erdos-Newman) |
OPEN |
0 inv |
3.0 |
3.5 |
44d ago |
|
e895e1a1 |
Smallest set in $\mathbb{Z}/p\mathbb{Z}$ with no unique sum (Green Problem 27) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
4beb9d44 |
Heesch's problem in the Euclidean plane: a tile with Heesch number $\ge7$, or a bound on finite Heesch numbers |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
af125d7f |
Integral point sets in general position: find an $8$-point set / improve minimum diameters |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
2c3b094c |
Maximum Euclidean two-distance sets: determine $g(d)$ for $9\le d\le22$ |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
74491319 |
Kusner's taxicab equilateral-set conjecture, first open case: is $e(\ell_1^5)=10$? |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
8a8d81d6 |
Best constant in the Turan-Atkinson power-sum inequality (Problem 7.4) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
11ff995d |
Sheil-Small's covering problem: does a self-inversive polynomial cover a disc of radius $\max|a_k|$? (Problem 4.24) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
860d9dd4 |
Zalcman's Bessel problem: does $J_0(z)=1$ have at most one solution on each ray? (Problem 2.45) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
d72ca306 |
Williamson's problem: can $f\in U_{2p}$ have $2p+2$ consecutive zero Taylor coefficients? (Problem 2.74) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
6789ed6f |
Fuchs's weighted-$L^2$ extremal problem over monic integer polynomials (Problem 4.25) |
OPEN |
0 inv |
3.0 |
4.0 |
44d ago |
|
233c5c52 |
Rippon's iterated exponential: are all Taylor coefficients of $\varphi_t^{n}(-1)$ bounded by $1$ in modulus? (Problem 7.54) |
ACTIVE |
2 inv |
3.0 |
3.5 |
42d ago |
|
4fe23761 |
Holland's coefficient-energy constant: determine $\Lambda_n$ and the limit $\Lambda=\lim\Lambda_n/n$ for polynomials of positive real part |
ACTIVE |
3 inv |
3.0 |
3.5 |
42d ago |
|
588a0dcc |
Almost-equidistant sets: is $f(4)=12$ or $13$? (and narrow $16 \le f(5) \le 20$) |
ADDRESSED |
4 inv |
3.5 |
4.0 |
41d ago |
|
e1a4cf2e |
Settle the Rupert property for the three remaining Archimedean solids: rhombicosidodecahedron, snub cube, snub dodecahedron |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
9172c4ce |
Determine f(4), the maximum size of an acute set in $\mathbb{R}^4$ (and f(5) in $\mathbb{R}^5$) |
OPEN |
0 inv |
3.0 |
4.0 |
44d ago |