Refined Inversion Statistics on Permutations

@article{Sack2012RefinedIS,
  title={Refined Inversion Statistics on Permutations},
  author={J. Sack and Henning {\'U}lfarsson},
  journal={Electron. J. Comb.},
  year={2012},
  volume={19},
  pages={P29}
}
We introduce and study new refinements of inversion statistics for permutations, such as $k$-step inversions, (the number of inversions with fixed position differences) and non-inversion sums (the sum of the differences of positions of the non-inversions of a permutation). We also provide a distribution function for non-inversion sums, a distribution function for $k$-step inversions that relates to the Eulerian polynomials, and special cases of distribution functions for other statistics we… Expand
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