A Survey of Alternating Permutations

@inproceedings{Stanley2010ASO,
  title={A Survey of Alternating Permutations},
  author={Richard P. Stanley},
  year={2010}
}
  • Richard P. Stanley
  • Published 2010
  • Mathematics
  • 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… CONTINUE READING

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