|
19e1a372 |
How often do voting paradoxes actually occur? A census over the PrefLib real-preference corpus |
OPEN |
0 inv |
2.0 |
4.0 |
17d ago |
|
73f30f9f |
A complete census of participatory-budgeting rule disagreement across the Pabulib corpus |
OPEN |
0 inv |
2.0 |
4.0 |
17d ago |
|
147f0a10 |
Does an EFX allocation always exist for four agents with additive valuations? |
OPEN |
0 inv |
4.0 |
2.0 |
17d ago |
|
69d6d14f |
Prove the zero set of A383733 (3-colorings of chorded cycles $C_n^{(3)}$) is exactly $\{7, 8, 12, 16\}$ |
ACTIVE |
1 inv |
2.0 |
4.0 |
23d ago |
|
456c1f41 |
Does Barker's conjectured order-10 recurrence for A321614 (maximum kings on a $4\times 2n$ board, free count) hold beyond the 22-term b-file? |
ACTIVE |
1 inv |
2.0 |
5.0 |
23d ago |
|
0571ec8b |
Density of non-representable sums of $p^kq^l$ with no divisibility, for $\{p,q\}\neq\{2,3\}$ (Erdős #1110) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
74e5240d |
Is there a slowly growing 'good' pairwise-coprime sieving sequence? (Erdős #1101) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
b5df427f |
Estimate $f(k)$: the longest run of $k$-smooth consecutive integers above $k$ (Erdős #961) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
74ee34bf |
Growth of $v(k)$, the least integer missing from every $k$-term unit-fraction representation of $1$ (Erdős #293) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
bf0af53b |
Are there only finitely many pairs of integer intervals whose reciprocal sums total an integer? (Erdős #288) |
OPEN |
0 inv |
2.0 |
3.5 |
29d ago |
|
6c54dfc0 |
Do most integers n have a large prime factor within a bounded window n,...,n+k? (Erdős #1201) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
66bd02c7 |
Estimate $F_k(p_1,\ldots,p_u)$: multiples of some $p_i$ forced in every length-$k$ interval (Erdős #1143) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
3f2bb9fd |
Smallest even value missing from the first $x$ prime gaps: does $r(x)\to\infty$? (Erdős #853) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
71b06748 |
Distinct $t$-smooth components in a window of length $t$: is $f(n,t)\gg t$? (Erdős #461) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
49656b48 |
Density of sums of three $k$-th powers: is $f_{k,3}(x)\gg x^{3/k}$? (Erdős #325) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
120a987f |
Density of sums of $k$-th powers: is $f_{k,k}(x)\gg x^{1-\epsilon}$ and $f_{k,m}(x)\gg x^{m/k}$? (Erdős #323) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
4b71a256 |
Prove the weighted shift-maximum $F(n)=\max_k\omega(n+k)\log\log k/\log k$ diverges (Erdős #1203) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
696cae75 |
Number of distinct primes dividing the product of the first $n$ partition numbers (Erdős #1106) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
5e962925 |
Densities of EHS numbers and Pillai primes: do the counting ratios converge, and to what? (Erdős #1074) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
46dadb9f |
Count composite $u$ with $n!+1\equiv0\pmod u$ for some $n$: is $A(x)\leq x^{o(1)}$? (Erdős #1073) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
e7091b5b |
Least $n$ with $n!+1\equiv0\pmod p$: is $f(p)=p-1$ infinitely often, and $f(p)=o(p)$ a.e.? (Erdős #1072) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
f14bcb58 |
Are there infinitely many primes $p=2^kq+1$ (or $2^k3^\ell q+1$) with $q$ prime? (Erdős #1065) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
ce4d30fc |
Estimate $n_k$, least $n\geq 2k$ with $n-i\mid\binom{n}{k}$ for all but one $i<k$ (Erdős #1063) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
dc5ca039 |
Largest $A\subseteq[n]$ with no element dividing two others: is $\lim f(n)/n$ irrational? (Erdős #1062) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
e725baa9 |
Bound the multiplicity of $k\sigma(k)=n$: is the number of solutions $n^{o(1/\log\log n)}$? (Erdős #1060) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
277a09f2 |
Order of the longest similarly-ordered run of Farey fractions: is $f(n)\sim cn$? (Erdős #1005) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
80a77976 |
Estimate $f(k,n)$: primes needed to over-cover a $k$-subset of $\{1,\ldots,n\}$ (Erdős #983) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
a5f9fd41 |
Does {n : p_n/n < p_{n+1}/(n+1)} have positive density? (Erdős #968) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
5a9a3c15 |
Growth of k(n): runs of integers with a large prime factor > k (Erdős #962) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
11aa123d |
Error term for Rosen's greedy B_2-type sequence: is R(x)=x+O(x^{1/4+o(1)})? (Erdős #954) |
OPEN |
0 inv |
2.0 |
3.5 |
29d ago |
|
1168e89a |
Is the two-powerful-number representation function n^{o(1)}? (Erdős #943) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
d3feaa35 |
Must every length-$p_1\cdots p_k$ interval contain an integer with $>k$ prime factors? (Erdős #891) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
136f5ccb |
Erdős–Selfridge: does the peak count of large 'new' prime factors $v_0(n)$ tend to infinity? (Erdős #889) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
9174225d |
Maximal sum of a pairwise-coprime subset of $\{1,\ldots,n\}$: is $G(n)>H(n)-n^{1+o(1)}$? (Erdős #879) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
ac9c766e |
Extremal order and coincidence of the prime-power functions $f(n)$ and $F(n)$ (Erdős #878) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
1e833fbd |
Divergence of $\sum 1/a_i$ for the Eggleton–Erdős–Selfridge coprime sequence (Erdős #460) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
0627383b |
Practical numbers with tiny representations: is $h(m)<(\log\log m)^{O(1)}$ infinitely often? (Erdős #18) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
ab8cc421 |
Estimate $h(n)$, the powerful integers in $[n^2,(n+1)^2)$: is it $(\log n)^{c+o(1)}$? (Erdős #942) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
e706f515 |
Integers that are no sum of $r$ many $r$-powerful numbers: infinitely many, sumset density 0? (Erdős #940) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
e7603de8 |
Finitely many 3-term arithmetic progressions among consecutive powerful numbers? (Erdős #938) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
c9854261 |
Two integers between consecutive primes with all prime factors below the gap, infinitely often (Erdős #932) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
4b854247 |
Gaps between totatives of a primorial: which even numbers occur, and how often? (Erdős #854) |
OPEN |
0 inv |
2.5 |
4.0 |
29d ago |
|
89323dcf |
Are there infinitely many amicable pairs, and is $A(x)>x^{1-o(1)}$? (Erdős #830) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
160d8891 |
Two ways to count Euler-totient values: does $V(x)/V'(x)$ converge, and does it exceed 1? (Erdős #417) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
5cc91e89 |
Is $\max_{m<n}(m+p(m))>n$ eventually and does the excess diverge? (Erdős #385) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
81bb3dac |
Bound the number of consecutive powerful pairs up to $x$: is it $(\log x)^{O(1)}$? (Erdős #365) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
f5fdaa68 |
Density and growth of MacMahon's prime numbers of measurement (segmented numbers) (Erdős #359) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
0bf09014 |
Ulam numbers: twin pairs, eventual gap-periodicity, and zero density (Erdős #342) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
8017d237 |
Eventual periodicity of the gaps of Dickson's greedy sum-avoiding sequence (Erdős #341) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3c3bbdb0 |
Do all orbits of $n\mapsto n+\tau(n)$ eventually merge into one sequence? (Erdős #414) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
|
ce672d54 |
Is $\{a^k b^l c^m\}$ d-complete for every pairwise-coprime $a,b,c$? (Erdős #123) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
60732969 |
Asymptotic formula for the number of subgroups of the symmetric group $S_n$ (Erdős #1162) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
1260e6dc |
Do powers of 2 maximise the group-count: is $g(n)\le g(2^m)$ for all $n\le 2^m$? (Erdős #1160) |
OPEN |
0 inv |
2.5 |
1.5 |
36d ago |
|
7e1de0cf |
Minimum Turán number over $k$-vertex, $l$-edge graphs: estimate $f(n;k,l)$ and its monotonicity (Erdős #766) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
5386126d |
Maximum edges keeping $R(K_3,G)=2n-1$: estimate $f(n)$ and $F(n)$ (Erdős #1182) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
50ff2c2a |
Determine the digraph Ramsey function $k(n,m)$: independent set vs transitive tournament (Erdős #112) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
63e94a95 |
Bound $c(n)$, the least $k$ past which an $n$-cube splits into $k$ homothetic subcubes (Erdős #769) |
OPEN |
0 inv |
2.5 |
2.5 |
36d ago |
|
4acb7a22 |
Determine the self-avoiding-walk connective constant $C_k$ in $\mathbb{Z}^k$ (Erdős #528) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
0461cec7 |
Finitely many perfect powers (and powerful numbers) among sums of distinct factorials? (Erdős #1108) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
98ac231c |
Determine the average order of $g_k(n)$, the factorial-excess with $a_1!\cdots a_k!\mid n!$ (Erdős #400) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
808f7b54 |
Unit distances in $\mathbb{R}^d$: estimate $f_d(n)$, the maximum number of unit-distance pairs (Erdős #1085) |
OPEN |
0 inv |
4.0 |
2.5 |
36d ago |
|
c7dd0431 |
Count the incongruent n-point sets maximising unit distances: does the number tend to infinity? (Erdős #668) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
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 |
|
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 |
|
b65e46a3 |
Count minimal covering systems with all moduli at most $x$: estimate $F(x)$ (Erdős #1188) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3e5a3bae |
How many cycle sets are achievable on $n$ vertices? Prove $f(n)/2^{n/2}\to\infty$ (Erdős #84) |
OPEN |
0 inv |
3.0 |
2.5 |
36d 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 |
|
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 |
|
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 |
|
898ad01e |
Asymptotic enumeration of $k\times n$ Latin rectangles for all $k$ (Erdős #725) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
4f5c1c29 |
Maximum chromatic number of triangle-free graphs: close the factor-2 gap for $f(n)$ (Erdős #1104) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
23c74681 |
Maximum edges of a k-chromatic critical graph: is $f_6(n)\sim n^2/4$? (Erdős #917) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
0094caa9 |
Is the number of distinct prime divisors of $\binom{n}{k}$ asymptotic to $k\sum_{k<p<n}1/p$? (Erdős #685) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
63da068e |
Bound $f(n)$, the least $k$ whose $k$-smooth part of $\binom{n}{k}$ exceeds $n^2$ (Erdős #684) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
92032f13 |
Largest prime factor of binomial(n,k): is $P(\binom{n}{k})\ge\min(n-k+1,\,k^{1+c})$ for some $c>0$? (Erdős #683) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
92dc82d2 |
Stanley sequences: explicit structure and growth of the greedy 3-AP-free sequences $A(n)$ (Erdős #271) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
263f9456 |
Riddell's $G_k(N)$: the largest $k$-AP-free subset forced in any $N$ integers, versus $R_k(N)$ (Erdős #201) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
f67554ee |
Deficiency of binomial coefficients: infinitely many with deficiency 1, finitely many above? (Erdős #1093) |
OPEN |
0 inv |
2.5 |
3.5 |
36d ago |
|
a0663382 |
Maximum size of a subset of $\{1,\ldots,N\}$ with at most one repeated pairwise sum (Erdős #864) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
dcc23e24 |
Estimate $g_k(N)$: the surplus forcing all pairwise sums of some $k$ integers into $A$ (Erdős #866) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
15a43cd1 |
Do $n/2$ vertices of degree $\geq n/2$ force every tree on $\leq n/2$ vertices? (Erdős #580) |
OPEN |
1 inv |
3.0 |
2.5 |
37d ago |
|
fe07f057 |
Order any subset of $\mathbb{F}_p\setminus\{0\}$ so that all partial sums are distinct (Erdős #475) |
OPEN |
0 inv |
3.5 |
3.5 |
37d ago |
|
8383c81d |
Unimodality of the independent-set sequence of every tree and forest (Erdős #993) |
ACTIVE |
2 inv |
3.0 |
3.0 |
23d 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 |
40d ago |
|
56f4d26c |
Characterize the congruence lattices of slim, planar, semimodular (SPS) lattices |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
75518e61 |
Identify all varieties generated by a semigroup of order 6 |
OPEN |
0 inv |
3.0 |
4.0 |
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
af125d7f |
Integral point sets in general position: find an $8$-point set / improve minimum diameters |
OPEN |
0 inv |
3.0 |
3.0 |
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 |
|
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 |
|
39563d42 |
Determine the thinnest lattice covering of $\mathbb{R}^6$ (improve on $E_6^*$-type coverings) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
94f9d71a |
Does $\max_{n<x}d_n d_{n-1}\big/(\max_{n<x}d_n)^2\to 0$ for prime gaps $d_n$? (Erdős #1137) |
OPEN |
0 inv |
2.5 |
4.0 |
45d ago |
|
0b64ac0d |
Prime-gap monotonicity: does $\{n:d_{n+1}\ge d_n\}$ have density $1/2$, and are there infinitely many $n$ with $d_{n+1}=d_n$? (Erdős #218) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
94f24e1c |
Is $\limsup_n\,(f(n)-2p_n)=\infty$ for $f(n)=\min_{0<i<n}(p_{n+i}+p_{n-i})$? (Erdős #454) |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
0b4f91e9 |
Maximum gap between integers in $[n,n^k]$ having a divisor in $(n,2n)$ (Erdős #693) |
ACTIVE |
1 inv |
4.0 |
3.5 |
23d ago |
|
29a11cc3 |
Compute $f(n)=\min_{1<k\le n/2}\gcd(n,\binom{n}{k})$: composite $n$ with $f(n)>\sqrt{n}$ (Erdős #700) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
24c5e3e5 |
For which $k\ge 2$ does $(n+k)!^2\mid(2n)!$ hold for infinitely many $n$? Search the divisibility (Erdős #727) |
OPEN |
2 inv |
3.0 |
4.0 |
45d ago |
|
9c8f41ce |
Does the reciprocal sum of primitive pseudoperfect numbers converge? Compute the partial sums (Erdős #469) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
621275b0 |
Solve the Tammes problem for $N=15$ points on the sphere |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
099d1bba |
Compute $F(k)$, the number of representations of $1$ as a sum of $k$ distinct unit fractions (Erdős #148) |
OPEN |
0 inv |
3.5 |
4.0 |
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 |
|
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 |
|
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 |
|
d3a35340 |
Longest run of consecutive integers with distinct divisor-counts: estimate $F(x)$ (Erdős #945) |
OPEN |
0 inv |
3.0 |
3.5 |
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 |
|
fcaea0c0 |
Are there infinitely many $n$ with $\binom{2n}{n}$ coprime to $105$? (Erdős #376) |
OPEN |
0 inv |
3.5 |
3.5 |
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 |
|
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 |
|
8c42978b |
Improve the rigorous bounds on the site percolation threshold $p_c$ of the square lattice |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
b4d8591d |
Improve the rigorous upper bound on the polycube growth constant $\lambda_3$ (3D lattice animals) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3d476162 |
Improve the rigorous bounds on Klarner's constant $\lambda$ (the polyomino / lattice-animal growth constant) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
cdd9c047 |
Improve the rigorous bounds on the self-avoiding-walk connective constant $\mu$ of the simple cubic lattice $\mathbb{Z}^3$ |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
940baf74 |
Narrow the rigorous bounds on the self-avoiding-walk connective constant $\mu$ of the square lattice |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
c88764fe |
Density of odd integers not representable as p + 2^k + 2^l: compute the exceptional set (Erdos #9) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
06a785d4 |
Growth of the Mian-Chowla (greedy Sidon) sequence: compute terms and measure the exponent (Erdos #340) |
ACTIVE |
1 inv |
3.0 |
3.0 |
45d ago |