{"schema":"vela.problem-packet.v0.1","problem":36,"statement":"Find the optimal constant $c>0$ such that the following holds. For all sufficiently large $N$, if $A\\sqcup B=\\{1,\\ldots,2N\\}$ is a partition into two equal parts, so that $\\lvert A\\rvert=\\lvert B\\rvert=N$, then there is some $x$ such that the number of solutions to $a-b=x$ with $a\\in A$ and $b\\in B$ is at least $cN$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A393584","name":"a(n) is the minimum, over all partitions {X, Y} of {1..2n} with |X| = |Y|, of the maximum number of pairs (x, y) with the same difference x - y for x in X and y in Y.","terms":"1,1,2,2,3,3,3,4,4,5,5,5,6,6,6,7,7,8,8,8,9,9,10,10,10,11,11,11,12,12,13,13,13","url":"https://oeis.org/A393584"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}