@article{49677beb4a7d414ca118e73d38132bbf,
title = "On the number of monotone sequences",
abstract = "One of the most classical results in Ramsey theory is the theorem of Erdos and Szekeres from 1935, which says that every sequence of more than k2 numbers contains a monotone subsequence of length k+1. We address the following natural question motivated by this result: Given integers k and n with n≥k2+1, how many monotone subsequences of length k+1 must every sequence of n numbers contain? We answer this question precisely for all sufficiently large k and n≤k2+ck3/2/log k, where c is some absolute positive constant.",
keywords = "Erdos-Rademacher, Erdos-Szekeres, Monotone subsequences, Supersaturation",
author = "Wojciech Samotij and Benny Sudakov",
note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",
year = "2015",
month = nov,
day = "1",
doi = "10.1016/j.jctb.2015.05.008",
language = "אנגלית",
volume = "115",
pages = "132--163",
journal = "Journal of Combinatorial Theory. Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",
}