This article is cited in 1 paper

Monotonic subsequences in permutations of $n$ natural numbers

B. S. Stechkin

M. V. Lomonosov Moscow State University

Abstract: Let $S_n$ be the set of all permutations of the numbers $1,2,\dots,n$, and let $l_n(\sigma)$ be the number of terms in the maximal monotonic subsequence contained in $\sigma\in S_n$. If $M(l_n(\sigma))$ is the mean value of $l_n(\sigma)$ on $S_n$, then, for all except a finite number of n, the bound $M(l_n(\sigma))\le e\sqrt n$ is valid.

UDC: 519.2

Received: 31.12.1971

 English version: Mathematical Notes, 1973, 13:4, 310–312

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