Problems

R_dih(P_3^alt, K_b) = R_cyc(P_3^alt, K_b) = 2b - 1 for all b ∈ N — the a = 3 slice of Conjecture 4.9 (Damnjanović–Đorđević, arXiv:2607.06817) and Conjecture 4.23 (Bašić–Damnjanović–Stevanović–Stošić, arXiv:2604.16188).

Let S(N) count the distinct values of ∑_n∈ A 1/n over A⊆1,…,N. Estimate S(N).

There exists a Hadamard matrix of order 668: a matrix H∈-1,1^668×668 such that HH^ T=668I_668. Equivalently, the 668 rows of H are pairwise orthogonal.

Conjectures that every bridgeless graph has a collection of cycles covering each edge exactly twice.

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

For a sequence of n distinct reals, determine the largest constant c such that some monotonic subsequence always has sum exceeding (c-o(1))·(1/√n) times the total sum. Resolved as c = 1.

If CT_(k) is generated by all horizontal class transpositions with modulus at most k, is CT_(k) ≅ S_lcm(2,…,k) for every k ≥ 4?

Crouzeix conjectured in 2004 that for every square complex matrix A and every polynomial p, lVert p(A)rVert ≤ 2 max_z ∈ W(A) |p(z)|, where W(A) is the numerical range of A - that is, the numerical range is a 2-spectral set. Crouzeix proved…

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.

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

For which lattice parameters does a totally positive window function generate a Gabor frame? Gröchenig and Stöckler initiated the program in 2013; this paper gives the complete characterization, together with a Kadets-type theorem for…

For a semistable one-parameter family of complex projective varieties with smooth nearby fiber X_t and monodromy T, is the map H^1(X, Z) → H^1(X_t, Z)^T surjective? True in degree one, although the integral statement fails in higher degree.

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.

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

For a finite connected graph G, let L_s(G) be the maximum number of leaves in a spanning tree and ℓ(G) the average local independence number. Must L_s(G) ≥ 2(ℓ(G) - 1)?

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