A Survey of Alternating Permutations
A Survey of Alternating Permutations
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DOI：
10.1090/conm/531/10466
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发表时间：
2009-12
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通讯作者：
R. Stanley
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文献类型：
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作者：
R. Stanley
排列a1a2···an为1，2，.，如果a1> a2 a4 <···，则n是交替的。本文从Andre的著名结果开始，对交替排列理论的某些方面进行了综述：如果En是1，2，…的交替排列的个数，n，则P n = 0 En x n n! = secx + tanx。主题包括改进和q-类似物的恩，各种出现的恩在数学中，最长的交替排列顺序，本影enumeration特殊类的交替排列，和交替排列之间的连接和cd指数的对称群。献给Reza Khosrovshahi在他70岁生日之际
A permutation a1a2 ···an of 1,2,...,n is alternating if a1 > a2 a4 < ···. We survey some aspects of the theory of alternating permu- tations, beginning with the famous result of Andre that if En is the number of alternating permutations of 1,2,...,n, then P n�0 En x n n! = secx + tanx. Topics include refinements and q-analogues of En, various occurrences of En in mathematics, longest alternating subsequences of permutations, umbral enu- meration of special classes of alternating permutations, and the connection between alternating permutations and the cd-index of the symmetric group. Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday