✦ LIBER ✦

Long unimodal subsequences: a problem of F.R.K. Chung

✍ Scribed by J.Michael Steele

Publisher: Elsevier Science
Year: 1981
Tongue: English
Weight: 285 KB
Volume: 33
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90168-0

No coin nor oath required. For personal study only.

✦ Synopsis

Let I(n) be the expected length of the longest unimodal subsequence of a random permutation. It is proved here that Z(n)/& converges to 24. This settles a conjecture of F.R.K. Chung. Let p denote a permutation of {1,2, . . . z n) and call (a, < a,*: l l l < q} a u?Gmxkzl subsequence provided there is a i such that p~~~)~pW~~ l l ~P(+Vwj+&=+' l *'PC& or PW > VW > l ' +P(+P&j+&= l l CPW-Let Z(n) denote the expe'cted length of the longest unimodal subsequence of a randomly permuted subsi:quence i.e. I(n) = xP p(p)/n!, where p(p) denotes the length of the longest unit nodal subsequence of the permutation p* F.R.K. Chung [l] conjixtured that lim :(n)/&= C exists.

📜 SIMILAR VOLUMES

On unimodal subsequences

✍ F.R.K Chung 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 557 KB

A Chung type law of the iterated logarit

A Chung type law of the iterated logarithm for subsequences of a Wiener process

✍ Qi-Man Shao 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 636 KB

A decision problem of long-term economic

A decision problem of long-term economic planning

✍ Péter Bod 📂 Article 📅 1966 🏛 Springer US 🌐 English ⚖ 443 KB

The model described in the present paper has been worked out to approximate a concrete problem of national economic planning. The problem presented itself in the daily practice of the National Planning Board of the Hungarian People's Republic in the course of a planning project carried out with the

An improved initial solution of a long t

An improved initial solution of a long transportation problem

✍ J. Intrator 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 403 KB

A Long Lonely Road, Return of the problem, book 41

✍ TJ Reeder 📂 Fiction 📅 2016 🏛 TJ Reeder 🌐 English ⚖ 62 KB 👁 1 views

Railway fatigue failures: an overview of

Railway fatigue failures: an overview of a long standing problem

✍ R. A. Smith 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 336 KB

## Abstract A wide ranging overview of fatigue problems in railway applications is presented. Concentration is focussed on fatigue problems specific to the railway industry, that is, those at or adjacent to the wheel‐rail interface. Consideration of wheels and rails leads to a discussion of the imp