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An interesting new Mahonian permutation statistic
The electronic journal of combinatorics, Tome 17 (2010)
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The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic DIS that is readily seen to be Mahonian. We give evidence showing that it is not equal to any previously published statistic. Nor does its joint distribution with the standard Eulerian statistics des and exc appear to coincide with any known Euler-Mahonian pair. A general construction of Skandera yields an Eulerian partner eul such that (eul, DIS) is equidistributed with (des, MAJ). However eul itself appears not to be a known Eulerian statistic. Several ideas for further research on this topic are listed.
DOI : 10.37236/419
Classification : 05A05
Mots-clés : generating random permutations, permutation statistics, Mahonian 
@article{10_37236_419,
     author = {Mark C. Wilson},
     title = {An interesting new {Mahonian} permutation statistic},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/419},
     zbl = {1204.05010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/419/}
}
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Mark C. Wilson. An interesting new Mahonian permutation statistic. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/419

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