{"schema":"vela.problem-packet.v0.1","problem":34,"statement":"For any permutation $\\pi\\in S_n$ of $\\{1,\\ldots,n\\}$ let $S(\\pi)$ count the number of distinct consecutive sums, that is, sums of the shape $\\sum_{u\\leq i\\leq v}\\pi(i)$. Is it true that\\[S(\\pi) = o(n^2)\\]for all $\\pi\\in S_n$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A234813","name":"Number of distinct integers of the form i+(i+1)+(i+2)+...+j, for 1 <= i <= j <= n.","terms":"1,3,5,9,12,16,21,27,33,40,47,55,63,70,77,89,101,110,123,134,146,159,171,186,200,214,229,245,260,275,293,312,329,349,369,","url":"https://oeis.org/A234813"},{"id":"A389241","name":"Maximum number of distinct consecutive sums of a permutation of [n].","terms":"0,1,3,6,9,13,19,25,32,39,47,56,66,77,89,100","url":"https://oeis.org/A389241"},{"id":"A390187","name":"Minimum number of distinct consecutive sums of a permutation of [n].","terms":"0,1,3,5,7,10,13,17,20,25,30,33,39,44,50,56,63,70,77","url":"https://oeis.org/A390187"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}