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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Signed words and permutations, I: A fundamental transformation


Authors: Dominique Foata and Guo-Niu Han
Journal: Proc. Amer. Math. Soc. 135 (2007), 31-40
MSC (2000): Primary 05A15, 05A30, 05E15
Published electronically: June 29, 2006
MathSciNet review: 2280171
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Abstract: The statistics major index and inversion number, usually defined on ordinary words, have their counterparts in signed words, namely the so-called flag-major index and flag-inversion number. We give the construction of a new transformation on those signed words that maps the former statistic onto the latter one. It is proved that the transformation also preserves two other set-statistics: the inverse ligne of route and the lower records.


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Additional Information

Dominique Foata
Affiliation: Institut Lothaire, 1 rue Murner, F-67000 Strasbourg, France
Email: foata@math.u-strasbg.fr

Guo-Niu Han
Affiliation: I.R.M.A. UMR 7501, Université Louis Pasteur et CNRS, 7 rue René-Descartes, F-67084 Strasbourg, France
Email: guoniu@math.u-strasbg.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08436-X
PII: S 0002-9939(06)08436-X
Keywords: Flag-inversion number, flag-major index, length function, signed permutations, signed words.
Received by editor(s): April 11, 2005
Received by editor(s) in revised form: August 4, 2005
Published electronically: June 29, 2006
Dedicated: This paper is dedicated to the memory of Percy Alexander MacMahon
Communicated by: John R. Stembridge
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.