A Conjecture of Stanley on Alternating Permutations

  title={A Conjecture of Stanley on Alternating Permutations},
  author={Robin J. Chapman and Lauren K. Williams},
  journal={Electron. J. Comb.},
We give two simple proofs of a conjecture of Richard Stanley concerning the equidistribution of derangements and alternating permutations with the maximal number of fixed points. 
On alternating signed permutations with the maximal number of fixed points
A conjecture by R. Stanley on a class of alternating permutations, which is proved by R. Chapman and L. Williams states that alternating permutations with the maximal number of fixed points is
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We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent
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Combinatorics of permutations
  • M. Bóna
  • Mathematics, Computer Science
  • 2008
This book discusses Permutations as Genome Rearrangements, algorithms and permutations, and the proof of the Stanley-Wilf Conjecture.
An (n1, n2, . . . , nk)-colored permutation is a permutation of n1 + n2 + · · ·+ nk in which 1, 2, . . . , n1 have color 1, and n1 + 1, n1 + 2, . . . , n1 + n2 have color 2, and so on. We give a
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Bivariate generating functions for permutations classified according to the numbers of mth descents and inversions are given and connections to the results on half-descents and alternating permutations are indicated.


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