一小时邀请报告简介之十五：登飞机的最快方法

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一小时邀请报告简介之十五：登飞机的最快方法
（转自2006年国际数学家大会官方网站）

Plenary lecture: Richard P. Stanley
The Quickest Way to Board an Aircraft

How many times on boarding a plane have you had to wait to reach your seat because the passengers in front of you are busy stowing their luggage? Did you always think that passengers with seats at the rear of the plane should board at the back and those with seats near the nose should board at the front? Well, in fact, this is not necessarily true, since it has been proved that this method is no more effective than letting everyone board at the same time. The best method is for the passengers with window seats to board first, those with centre seats second, and those with aisle seats last of all. This is just one of the applications of mathematics to daily life deriving from the study of sub-sequences, a subject Richard P. Stanley will speak about at one of the plenary lectures during the International Congress of Mathematicians this coming August in Madrid.

“Increasing and decreasing subsequences are very simple concepts” Stanley says. He asks you to choose at random a sequence of different numbers; for example, 2, 7, 1, 3, 8, 5. The elements on which the Stanley’s lecture will concentrate are the subsets of numbers belonging to the sequence which either appear in increasing order; for example, 2, 7 or 1, 3, 5, or which appear in decreasing order; for example, 2, 1 or 8, 5. As this mathematician from the MIT explains: “One of the most interesting aspects of increasing and decreasing subsequences is the length of the longest of such subsequences”. In the first sequence, we can find several increasing subsequences of 3 elements: 2, 7, 8; 2, 3, 5 or 1, 3, 5, but none of length 4. The first result proven in relation to these sub-sequences comes from Erdos and Szekeres and states that the product of the length of the longest increasing subsequence and the length of the longest decreasing subsequence is at least as large as the total number of terms in the original sequence.

Results such as this form part of the study of these sequences, and as Stanley points out, “one of the most interesting features of increasing and decreasing subsequences is their unexpected connection with other areas of mathematics, such as representation theory and random matrices”, which if applied to the “real world” translate into examples such as passengers boarding an airplane.

Richard P. Stanley was born in 1944. He concluded his degree in mathematics at the California Institute of Technology in 1966, and in 1971 he obtained his PhD from Harvard University. In 1973 he began to work in the MIT, where since the year 2000 he has been the Norman Levinson Professor of Applied Mathematics. He has received much recognition for his work, his most recent awards being the Rolf Schock Prize in 2003, and his appointment as Senior Scholar of the Clay Mathematics Institute in 2004. Since 1995 he has been a member of the USA National Academy of Sciences.

Speaker: Richard P. Stanley
Title: Increasing and Decreasing Sub-sequences
Date: Thursday, 24 August: 09:00-10:00
（转自2006年国际数学家大会官方网站）