|
91ef483a |
Improve or verify the best-known [48,24] linear code over GF(5): current bounds 15 ≤ d ≤ 20 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
ef6668dc |
Improve or verify the best-known [60,30] linear code over GF(4): current bounds 17 ≤ d ≤ 23 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
76d3c274 |
Improve or verify the best-known [80,40] linear code over GF(3): current bounds 19 ≤ d ≤ 26 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
97335ef7 |
Improve the bounds on the kissing number $K(5)$ in dimension 5 |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
5d1354f0 |
Improve or verify the best-known [128,64] binary linear code: current bounds 22 ≤ d ≤ 28 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
91e1a8c1 |
Smallest $n$ admitting an antichain on $[n]$ with $n-3$ distinct block sizes, each used $\ge r$ times (Erdős #776) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
f10b471f |
Estimate $f(n)$: the fewest subsets in convex position among $n$ points in general position (Erdős #838) |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
a6f7ac3a |
Raise the lower bound for the multicolour Ramsey number $R(3,3,3,3)$ beyond 51 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
b12da8db |
Compute $\alpha_4(n)$: the largest general-position subset forced among $n$ points with no 4 on a line (Erdős #589) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
8f947a57 |
Improve or certify optimal Heilbronn triangle configurations for $n\ge 10$ points (Erdős #507) |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
28325c3a |
Construct or bound the largest isosceles set in $\mathbb{R}^9$ (Erdős #503) |
OPEN |
0 inv |
2.5 |
2.0 |
45d ago |
|
3947e2bd |
Improve lower bounds on $N(n)$, the maximum number of mutually orthogonal Latin squares, for small orders (Erdős #724) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
d3f8ebf5 |
Determine or bound $m(5)$: fewest edges in a non-2-colorable 5-uniform hypergraph (Erdős #901) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
330fca99 |
Verify Chvátal's conjecture on intersecting families in downsets for the 8-element ground set (Erdős #701) |
OPEN |
0 inv |
3.5 |
2.0 |
45d ago |
|
e504203e |
Improve the lower bound on the sixth Busy Beaver value S(6)/Sigma(6) for 2-symbol Turing machines |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
1a93a941 |
Determine the maximum multiplicative complexity of a 7-variable Boolean function (does one need >= 8 AND gates?) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
716dd457 |
Find a synchronizing automaton with reset threshold exceeding (n-1)^2, or extend Cerny verification to n=13 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
9a466da8 |
Improve the bounds on the football-pool number K_3(6): ternary covering code of length 6, radius 1 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3314beef |
Is 47 multiplications optimal for 4x4 matrix multiplication over GF(2)? Beat AlphaTensor's rank-47 scheme |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
8996def9 |
Reduce the rank of the 3x3 matrix multiplication tensor below 23 (or improve the lower bound above 19) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
49dff27d |
Improve the best-known longest coil (coil-in-the-box) in the 9-dimensional hypercube beyond length 188 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
78e7d60c |
Improve the best-known longest snake (snake-in-the-box) in the 9-dimensional hypercube beyond length 190 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3f19c4cf |
Close the gap for the minimal superpermutation length on 6 symbols: 867 <= s(6) <= 872 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
258584fb |
Determine the optimal depth of a sorting network on 18 channels: does a depth-10 network exist? |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3a9219bd |
Improve the best-known size (comparator count) of a sorting network on 13 inputs below 45 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
facb9007 |
Do any three longest paths in a connected graph share a common vertex? |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
30b9eaa1 |
Compute the maximum size of a 3-sunflower-free $n$-uniform family for small $n$ (Erdős #20) |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
63f5643b |
Consecutive gaps in the sequence of sums of two squares: bound $n_{k+1}-n_k$ (Erdős #222) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
18612809 |
Integers $n$ with $m+\omega(m)\le n$ for all $m<n$: are there infinitely many? (Erdős #413) |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
3991b79b |
Harmonic-sum numerator vs. $\mathrm{lcm}(1,\ldots,n)$: do coprime and non-coprime cases each occur infinitely often? (Erdős #291) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
d3db87f6 |
Distinct exponents in the prime factorisation of $n!$: is $h(n)\sim c\sqrt{n/\log n}$? (Erdős #912) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
d3a35340 |
Longest run of consecutive integers with distinct divisor-counts: estimate $F(x)$ (Erdős #945) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
dbbf6e91 |
Search for a counterexample to $\pi(x+y)\le\pi(x)+\pi(y)$ (second Hardy–Littlewood conjecture, Erdős #855) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
5c5bb436 |
How small can a maximal Sidon subset of $\{1,\ldots,N\}$ be? (Erdős #156) |
OPEN |
0 inv |
4.0 |
2.5 |
45d ago |
|
759166b5 |
Count the distinct subset-sums of $\{1,\tfrac12,\ldots,\tfrac1N\}$: extend the sequence $S(N)$ (Erdős #320) |
OPEN |
0 inv |
2.5 |
3.0 |
45d ago |
|
46a97df5 |
Does the number of distinct values of $k!\bmod p$ approach $(1-1/e)p$? (Erdős #478) |
OPEN |
0 inv |
3.5 |
3.0 |
45d ago |
|
fcaea0c0 |
Are there infinitely many $n$ with $\binom{2n}{n}$ coprime to $105$? (Erdős #376) |
OPEN |
0 inv |
3.5 |
3.5 |
45d ago |
|
9bb63a76 |
Find three consecutive pairs of integers with matching prime support (Erdős #850) |
OPEN |
0 inv |
2.5 |
3.0 |
45d ago |
|
65904f16 |
Search for an odd weird number, or extend the sequence of primitive weird numbers (Erdős #470) |
OPEN |
0 inv |
3.0 |
2.5 |
45d ago |
|
83ebe9db |
Acyclic Edge Coloring Conjecture: does every graph have an acyclic edge coloring with Δ + 2 colors? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
b38e9211 |
3-Decomposition Conjecture: does every connected cubic graph split into a spanning tree, a matching, and cycles? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
8a267a3b |
Reconstruction Conjecture: is every graph on ≥3 vertices determined by its deck of vertex-deleted subgraphs? |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
8949994e |
Van Dam–Haemers Conjecture: are almost all graphs determined by their adjacency spectrum? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
5a7b263a |
Jørgensen's Conjecture: is every 6-connected graph with no K_6 minor apex? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
96c35e88 |
Total Coloring Conjecture: is the total chromatic number of every graph at most Δ + 2? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
f75dd724 |
Borodin–Kostochka Conjecture: for Δ ≥ 9, does no K_Δ force χ ≤ Δ − 1? |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
b6b9fcf5 |
Is the star chromatic index of every subcubic graph at most 6? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
a44c567c |
Gallai's Path Decomposition Conjecture: can every connected n-vertex graph be split into ⌈n/2⌉ paths? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
96f0741c |
Cycle Double Cover Conjecture: does every bridgeless graph have cycles covering each edge exactly twice? |
OPEN |
0 inv |
5.0 |
2.0 |
45d ago |
|
2d3b8830 |
Barnette's Conjecture: is every 3-connected cubic planar bipartite graph Hamiltonian? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |