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CATEGORIES:Academics,Lectures/Seminars
DESCRIPTION:Speaker: Professor Richard Stanley\, MIT\n\nAbstract:\n\nA perm
utation a1 a2 ··· an is alternating if a1 > a2 < a3 > a4 < a5 > ···. If En
is the number of alternating permutations of 1\, 2\, ...\, n\, then n 0 En
xn (n!)-1 = sec x + tan x. We will discuss several aspects of the theory o
f alternating permutations. Some occurences of the numbers En\, such as cou
nting orbits of group actions and volumes of polytopes\, will be surveyed.
The behavior of the length of the longest alternating subsequence of a rand
om permutation will be analyzed\, in analogy to the length of the longest i
ncreasing subsequence. We will also explain how various classes of alternat
ing permutations\, such as those that are also fixed-point free involutions
\, can by counted using a certain representation of the symmetric group Sn
whose dimension is En.
DTEND:20160930T180000Z
DTSTAMP:20230610T222733Z
DTSTART:20160930T170500Z
GEO:47.118149;-88.546013
LOCATION:Fisher Hall\, 138
SEQUENCE:0
SUMMARY:A survey of alternating permutations
UID:tag:localist.com\,2008:EventInstance_2325455
URL:https://events.mtu.edu/event/a_survey_of_alternating_permutations
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