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Ballantine, Beck, Feigon and Maurischat introduced the subsum polynomial sp(λ,x) := ∏_i (1+x^λ_i) attached to an integer partition λ, studied rational functions built by summing reciprocals of these polynomials over natural classes of…

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

If A is a forbidden-divisor set with |A ∩ [1,x]| = o(√x) and B = b_1 < b_2 < … the sifted set, must x^-1 ∑_b_i < x (b_i+1 - b_i)^2 converge to a finite limit?

If h(r) is the maximal finite exact order attainable by an additive basis of order at most r, what is lim_r → ∞ h(r)/r^2? The candidate proof identifies the sharp limit 1/3.

Do a finite group's order together with ∑_g ∈ G φ(|g|) determine whether the group is simple? A simple and a non-simple group of order 6048 share the statistic 23984.

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?

Must the right-relatively convex subgroups of a right-orderable nonabelian group form a sublattice of its subgroup lattice? A construction shows they need not.

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…

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

Can a complete edge-coloured, complex-weighted graph realize perfect-matching amplitudes of one on every monochromatic inherited vertex colouring and zero otherwise? Nonexistence is proved in the diagonal family N = D for every even N ≥ 4,…

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 R(3;k) be the least n such that every k-colouring of the edges of K_n contains a monochromatic triangle. Determine lim_k→∞ R(3;k)^1/k (a $250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is…

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)?