Lean 4 formalization proves Singer's Sidon-set construction for every prime power and builds a library that yields unconditional two-sided bounds h(N)=Θ(√N) plus a conditional route to the full Erdős Problem 30 asymptotic.
and Harman, Glyn and Pintz, J\'anos , TITLE =
6 Pith papers cite this work, alongside 419 external citations. Polarity classification is still indexing.
6
Pith papers citing it
419
external citations · OpenAlex
years
2026 6representative citing papers
Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
g(n) ≪_ε n^{ρ+ε} with ρ = (13 - √69)/10 < 0.47 for multiplicative Sidon sets that intersect every interval of length L up to n.
H(k)^{1/k}/k = Ω(k/log k) as k→∞, resolving the positive direction of Erdős-Graham problem #190.
π_link(t) ≤ 1 - t^{-1} - t^{-2}/12 for every t ≥ 2, which determines the order of the gap to the trivial bound 1 - t^{-1} up to a constant factor when paired with Goldwasser's lower bound for prime-power t-1.
For almost all x, the interval (x, x+h] with h=X^θ contains ≍h integers that are a prime plus an element of the lacunary sumset Aλ, for every θ>2/15+ε.
citing papers explorer
-
Formalizing Singer Sidon Constructions and Sidon Set Infrastructure in Lean 4
Lean 4 formalization proves Singer's Sidon-set construction for every prime power and builds a library that yields unconditional two-sided bounds h(N)=Θ(√N) plus a conditional route to the full Erdős Problem 30 asymptotic.
-
Counting Small Induced Subgraphs: Hardness of Symmetry-Based Properties
Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
-
Gaps in Multiplicative Sidon Sets
g(n) ≪_ε n^{ρ+ε} with ρ = (13 - √69)/10 < 0.47 for multiplicative Sidon sets that intersect every interval of length L up to n.
-
A resolution of Erd\H{o}s Problem #190 via Erd\H{o}s-Lov\'asz, BCT, and Baker-Harman-Pintz
H(k)^{1/k}/k = Ω(k/log k) as k→∞, resolving the positive direction of Erdős-Graham problem #190.
-
A note on the $t$-partite link problem of F\"uredi
π_link(t) ≤ 1 - t^{-1} - t^{-2}/12 for every t ≥ 2, which determines the order of the gap to the trivial bound 1 - t^{-1} up to a constant factor when paired with Goldwasser's lower bound for prime-power t-1.
-
Short intervals for the Romanoff-type sumset
For almost all x, the interval (x, x+h] with h=X^θ contains ≍h integers that are a prime plus an element of the lacunary sumset Aλ, for every θ>2/15+ε.