@article{ff959760520740af895314046651f150,
title = "A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets",
abstract = "We present a simple transformation for the inversion number and major index statistics on the labelings of a rooted tree with n vertices in the form of a rake with k teeth. The special case k= 0 provides a simple transformation for the Mahonian statistics on the set Sn of permutations of { 1 , 2 , ⋯ , n}. We also extend the transformation to a bijective interpretation of the fact that the major index of the equivalence classes of the labelings is equidistributed with the major index of the permutations in Sn satisfying the condition that the elements 1 , 2 , ⋯ , k appear in increasing order.",
keywords = "Bijection, Mahonian statistics, Rake poset, Subexcedent word",
author = "Eu, {Sen Peng} and Fu, {Tung Shan} and Hsu, {Hsiang Chun}",
note = "Funding Information: Acknowledgements The authors thank the referees for helpful suggestions. This research is partially supported by MOST Grants 104-2115-M-003-014-MY3 (S.-P. Eu), 105-2115-M-153-002-MY2 (T.-S. Fu) and MOST postdoctoral fellowship 106-2811-M-003-011 (H.-C. Hsu). Publisher Copyright: {\textcopyright} 2018, Springer Japan KK, part of Springer Nature.",
year = "2018",
month = mar,
day = "1",
doi = "10.1007/s00373-018-1882-z",
language = "English",
volume = "34",
pages = "373--381",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer Japan",
number = "2",
}