Inversion-descent polynomials for restricted permutations

@article{Graham2013InversiondescentPF,
  title={Inversion-descent polynomials for restricted permutations},
  author={Fan Chung Graham and Ronald L. Graham},
  journal={J. Comb. Theory, Ser. A},
  year={2013},
  volume={120},
  pages={366-378}
}
We derive generating functions for a variety of distributions of joint permutation statistics all of which involve a bound on the maximum drop size of a permutation @p, i.e., max{i-@p(i)}. Our main result treats the case for the joint distribution of the number of inversions, the number of descents and the maximum drop size of permutations on [n]={1,2,...,n}. A special case of this (ignoring the number of inversions) connects with earlier work of Claesson, Dukes and the authors on descent… CONTINUE READING

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