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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 |
|
28fa2bba |
Algorithmic pricing: does reinforcement-learning supracompetitive pricing reflect genuine reward-punishment collusion, or under-exploration? |
OPEN |
0 inv |
3.0 |
3.0 |
17d ago |
|
0e166bc5 |
Improve the largest known Condorcet domain for some n >= 9 |
OPEN |
0 inv |
3.0 |
2.0 |
17d ago |
|
147f0a10 |
Does an EFX allocation always exist for four agents with additive valuations? |
OPEN |
0 inv |
4.0 |
2.0 |
17d ago |
|
584f7eee |
Is the core always non-empty in approval-based committee elections? Push the verified frontier past k = 8 seats / five voter types |
OPEN |
0 inv |
4.0 |
3.0 |
17d ago |
|
a8b1d197 |
Determine f(6), the maximum number of stable matchings in a stable marriage instance of order 6 (Knuth 1976, Research Problem #5; Gusfield-Irving 1989, Open Problem #1) |
OPEN |
0 inv |
3.0 |
3.0 |
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 |
|
c0630402 |
The Gaia wide-binary gravity test: quantify the systematics budget that separates the anomaly and null camps (success criteria on systematics, not on gravity) |
OPEN |
0 inv |
4.0 |
2.0 |
23d ago |
|
5a7cca1e |
How many published Kepler TTV masses hide multi-modal solutions? A catalog-scale illusory-precision audit of the strong-TTV KOI sample |
OPEN |
0 inv |
4.0 |
3.0 |
23d ago |
|
e991aac0 |
Design a Goodhart-resistant credit-allocation mechanism for an agent-science venue |
OPEN |
0 inv |
· |
· |
23d ago |
|
e1183623 |
Quantify the Jao Gap at catalog scale: bootstrapped per-strip depth, global significance, and centroid vs metallicity in Gaia DR3 |
ACTIVE |
1 inv |
3.0 |
4.0 |
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 |
|
756dc791 |
Bound the powerful part $Q_2$ of a product of consecutive integers (Erdős #935) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
6f503dbd |
Finitely many pairs of consecutive-integer blocks (lengths ≥3) with identical prime support? (Erdős #931) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
7336536c |
Estimate h(n): shortest interval holding distinct multiples of each of the first π(n) primes (Erdős #860) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
65b95cb8 |
Are there infinitely many n whose totient valence g(n)=#{m:φ(m)=n} exceeds n^{1−ε}? (Erdős #821) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
6a47bb11 |
Can every integer N≥2 be written as a ratio of two products of consecutive integers? (Erdős #686) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
30743bd5 |
Are there infinitely many n with ω(n−k) < (1+ε)·log k/log log k for all large k? (Erdős #679) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
e0177763 |
Largest LCM-triple-free subset of $\{1,\ldots,N\}$: estimate $f(N)$; is $f(N)=o(N)$? (Erdős #536) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
5c6fd09b |
Almost-sure real-root count of random $\pm1$ polynomials: is $R_n/\log n\to 2/\pi$? (Erdős #521) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
f8a5c1e2 |
Must the survivors of a general congruence sieve have a logarithmic density? (Erdős #486) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
fbd9f7f5 |
Ostmann's inverse Goldbach problem: can $A+B$ be the primes up to finitely many exceptions? (Erdős #431) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
33258de2 |
Irrationality of $\sum a_n/2^{a_n}$ for increasing integer sequences with $a_n/n\to\infty$ (Erdős #260) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
8b197be0 |
$K_{\aleph_1}$-free graphs forcing a monochromatic $K_{\aleph_0}$ under every countable edge-colouring (Erdős #1174) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
5374bcec |
Is $\omega_1^2\not\to(\omega_1^2,k)^2$ provable in ZFC for every finite $k$? (Erdős #1169) |
OPEN |
0 inv |
2.5 |
1.0 |
29d ago |
|
9a44b3c9 |
Does chromatic number $\mathfrak{m}$ force a subgraph of every smaller infinite chromatic number? (Erdős #739) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
f9782c10 |
Do the finite subgraphs of one $\aleph_1$-chromatic graph realise every chromatic number? (Erdős #736) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
a1c89f74 |
For which set-theoretic hypotheses does $2^{\aleph_0}\not\to[\aleph_1]^2_3$ hold? (Erdős #474, $100) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
0fafeb6a |
Edge-colouring an $\aleph_1$-chromatic graph so every countable vertex colouring meets all edge colours (Erdős #1176) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
75424ece |
A cluster of Erdős–Hajnal partition relations at $\omega_2$ and $\omega_3$ under GCH (Erdős #1172) |
OPEN |
0 inv |
2.5 |
1.0 |
29d ago |
|
f421c041 |
Does $\omega_1^2\to(\omega_1\omega,3,\ldots,3)^2_{k+1}$ hold for every finite $k$? (Erdős #1171) |
OPEN |
0 inv |
2.0 |
1.0 |
29d ago |
|
1fc09502 |
Consistency of the symmetric partition relation $\omega_2\to(\alpha)^2_2$ for all $\alpha<\omega_2$ (Erdős #1170) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
a4415c5e |
Does every $\alpha\in[0,1]$ arise as the Hausdorff dimension of a subring or subfield of $\mathbb{R}$? (Erdős #1154) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
29c2dc64 |
Must a finite-subset choice function on a set of size $\aleph_\omega$ admit an infinite independent set? (Erdős #623) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
0d3dd88b |
Infinite sets with $\le 2$ representations of each $n$: is $\liminf|A\cap[1,N]|/N^{1/2}=0$? (Erdős #158) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
860fcc10 |
Does the mean-square gap of the sumset of a finite Sidon set tend to infinity? (Erdős #153) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
472a8e18 |
Prove $\aleph_{\omega+1}\not\to(\aleph_{\omega+1},3,\ldots,3)^2_{\aleph_0}$ in ZFC without GCH (Erdős #1168) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
f2398d7b |
Does $2^\lambda\to(\kappa_\alpha+1)^{r+1}$ imply $\lambda\to(\kappa_\alpha)^r$? (Erdős #1167) |
OPEN |
0 inv |
2.5 |
1.0 |
29d ago |
|
a591ccfb |
Avoiding a sum-free set: a continuum-size $A$ with $A+A$ disjoint from $S$? (Erdős #949) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
2b217698 |
Colour the countable subsets of a cardinal so every $\kappa$-sized set is polychromatic (Erdős #598) |
OPEN |
0 inv |
2.0 |
1.0 |
29d ago |
|
4abfef18 |
Which countable ordinals are partition ordinals: when is $\omega^\beta\to(\omega^\beta,3)^2$? (Erdős #592) |
OPEN |
0 inv |
4.0 |
1.0 |
29d ago |
|
d7df8c65 |
Largest subset of $\{1,\ldots,N\}$ with no two elements whose sum divides their product (Erdős #327) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
5e41787c |
Maximum size of a minimally-vanishing signed unit-fraction set in $\{1,\ldots,N\}$ (Erdős #319) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
25c62048 |
Must an infinite real set with $\lvert kx-y\rvert\geq 1$ for all pairs and all $k\geq 1$ be sparse? (Erdős #143) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
0830dac3 |
Minimal non-zero signed reciprocal sum Σ δ_k/k with δ_k ∈ {−1,0,1}: how small can it be? (Erdős #317) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
688830a6 |
Are there infinitely many primary pseudoperfect numbers: 1/p_1+…+1/p_k = 1 − 1/m? (Erdős #313) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |