Problems

Is computing a Kemeny-optimal aggregate ranking NP-hard when the input consists of exactly three complete rankings? Hardness was known for every even n ≥ 4; three voters was the minimal open case, and n = 2 is polynomial-time solvable.

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For the switch-walk-switch lamplighter walk on Z_2 wr T_d, prove the sharp asymptotic p_2n(e,e) = ρ_d^2n exp[-(π^2 (log(d-1))^2 + o(1)) n/log^2 n] with ρ_d = frac2√d-1d.

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VibeMathed records no statement for this problem. See erdosproblems.com for the original.

For an even cycle of size N and depth p with 2p + 2 ≤ N, is the optimal QAOA approximation ratio for MaxCut exactly 2p+1/2p+2, as Farhi, Goldstone and Gutmann conjectured?

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VibeMathed records no statement for this problem. See erdosproblems.com for the original.

In the circle of Kummer's regular primes and Vandiver's conjecture, the paper proves that almost all primes are partially regular, yielding a partial Vandiver theorem for a density-one set of primes, with consequences for Kubota-Leopoldt…

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 p be a complex polynomial of degree n ≥ 2 whose zeros all lie in the closed unit disk. Then for every zero a of p, there exists a critical point ζ of p such that |ζ-a| ≤ 1. This is the standard Sendov statement and exactly matches the…

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.

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.

For the switch-walk-switch walk on Z_2 wr Z started at (0,0) and (0,2), prove |P_t^x - P_t^y|_TV asymp t^-1/2.

For smooth convex-concave min-max problems, can anchored gradient descent-ascent be scheduled so that its exact last-iterate squared-gradient residual is O(1/t), closing the gap left by the 2019 analysis?

R_dih(P_a^alt, K_b) = 1 + (a-1)(b-1) for all a ≥ 4, b ≥ 1 — the a ≥ 4 slice of Conjecture 4.9 (Damnjanović–Đorđević, arXiv:2607.06817). Combined with the a = 3 case (see sibling entry), this resolves Conjecture 4.9 in full for a ≥ 3.

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.