Problems
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VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Does the conjectured universal formula for normalized alternating syzygy power sums of numerical semigroup rings hold for every index?
Sixteen previously unknown exact values, plus three that confirm the sibling theorem entries' predictions computationally, across five ordered-pattern families (P^alt, S^sc, C^mon, M^nest, K) under dihedral and reflective group actions -…
For unit-modulus complex numbers z_i, let p_n(z)=∏_i≤ n(z-z_i) and M_n=max_|z|=1|p_n(z)|. Erdős's prize question: is there c>0 with ∑_k≤ n M_k > n^1+c?
For odd k with gcd(n,k) = gcd(n+1,k) = 1, is N_k(n) ≡ ⌊ (k+1)/4 ⌋ pmod 2, where N_k(n) counts pairs 1 ≤ b_i ≤ (k-1)/2 with b_1 + b_2 ≥ (k+1)/2 and b_2 ≡ n b_1 pmod k? Conjectured by Chen and Gendron; its proof removes a conditional step in…
If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four - that is, is every cograph power graph chordal?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Let a,b,c>1 be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form a^k b^l c^m (k,l,m≥ 0), none dividing another?
Is the number of nonnesting permutations of 1,1,…,n,n avoiding both 1132 and 3312 equal to 3^n - 3 · 2^n-1 + 1 for every n ≥ 1?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Let X = (X_1,…,X_n) be a centered Gaussian vector, not necessarily nondegenerate. Then, for every α_1,…,α_n > 0, E[∏_i=1^n |X_i|^α_i] ≥ ∏_i=1^n E[|X_i|^α_i]. Moreover, if Var(X_i) > 0 for every i, then equality holds if and only if…
The multivariate independence polynomial is the partition function of the hard-core model with per-vertex fugacities. The paper proves a lower bound extending to the multivariate setting a result Tao proved in the univariate case, and…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For positive integers d and k, let n_k(d) be the maximum order of a graph of maximum degree at most d and diameter at most k. It is shown that lim_d → ∞n_k(d)/d^k = 1 for every fixed k, thereby resolving the asymptotic degree-diameter…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.