Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
63 problems
For D_3(m) = vecC_m square vecC_m square vecC_m, can the full arc set be partitioned into three directed Hamilton cycles for every integer m ≥ 3?
A cyclic meander induces a cyclic permutation on its 2n marked intersection points. Schwartz's conjecture on the quadratic growth of the associated meander number is resolved.
For every finite connected graph, is girth(G) + 1 at most the product of its largest induced-tree order and its second-smallest degree?
For an inclusion-free hypergraph on n vertices, a weight assignment w:[n]→[d] is isolating when a unique edge attains minimum weight. Faber and Harris conjectured that the number of isolating assignments is at least n∑_j=0^d-1 j^n-1,…
Norine conjectured that every red-blue edge-colouring of the n-dimensional hypercube Q_n in which antipodal edges get opposite colours contains a monochromatic path from some vertex to its antipode. The paper proves it, via a chain-level…
Regts and Sevenster conjectured that a complex-valued graph parameter f with f(∅)=1 has exponentially bounded edge-connection rank precisely when it is a mixed partition function. The paper proves it, with the numbers of even and odd…
Amdeberhan, Shareshian and Stanley showed a function from the theory of partition Eisenstein series counts alternating permutations with a given record partition, and asked whether a similar theory exists for record compositions,…
Ji, Li and Wang conjectured in 2024 that every parallel chip-firing game on a finite connected graph whose chip count lies strictly between 2|E|-|V| and 2|E| has period exactly 2, generalizing the middle rung of Levine's devil's staircase…
A question of Averkov, Hofscheier and Nill on whether the Ehrhart h^*-polynomial of a lattice polytope of large lattice width is real-rooted. Proved in fixed dimension for sufficiently large lattice width, giving strict log-concavity and…
Zhu, Gyori, He, Lv, Salia and Xiao conjectured the maximum number of copies of a fixed cycle in an n-vertex graph of bounded circumference, attained by the join of a clique with an independent set. For every fixed s ≥ 3 and L ≥ 2s+2 and…
A subset A of the pointwise-ordered cube [0,1]^n is a k-antichain when it meets every chain in at most k points. The conjecture concerns the largest possible (n-1)-dimensional Hausdorff measure of such a set; it is settled here, following…
A tournament orients every pair in a round-robin (winner → loser). The score sequence is the sorted win-count list. Reversing a directed 3-cycle never changes scores, so score-equivalent tournaments can look structurally different.…
Godara and Sarkar proved d(H_27)=6 for the exponent-p Heisenberg group and posed d(H_p^3)=3p-3 for every odd prime p, leaving p≥5 open. The paper settles the first open case, d(H_125)=12, the upper bound reducing to a finite spread bound…
Let H(n) be the largest number of vertices in a hypergraph with no isolated vertices and no partition of size greater than n. With k_1 = 1 and k_n = ⌊ n/2 ⌋ + k_⌊ n/2 ⌋ + k_⌈ n/2 ⌉, prove H(n) ≥ c k_n for some constant c > 1, already for n…
A t-(v,k,λ) covering is a family of k-subsets of a v-set meeting every t-subset at least λ times, and C(v,k,t) is the least number of blocks. The recorded bounds for C(12,6,4) were 40 ≤ C(12,6,4) ≤ 41. No 4-(12,6,1) covering with 40 blocks…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Escobar, Klein and Weigandt proved that gradedness of an ASM weak order interval, constancy of Coxeter length across its fibres, and equidimensionality of the associated ASM varieties are mutually equivalent, and conjectured (Conjecture…
The imbalance of an edge uv of a finite simple graph is the absolute difference of the degrees of u and v. Kozerenko and Skochko conjectured that the multiset of all edge imbalances is graphic - realizable as the degree sequence of some…
A generalization of Boppana's entropy inequality, of the kind used in union-closed-sets arguments, proved and formalized: the sharp form with the extremal constant characterized via the unique positive solution of an explicit equation.
A collection of open problems from the algebraic and enumerative combinatorics literature, resolved in one paper: a conjecture of Defant, Jiang, Marczinzik, Segovia, Speyer, Thomas and Williams on the echelonmotion operator on modular…