Séminaire Lotharingien de Combinatoire, B62c (2010), 10 pp.
Hilarion L. M. Faliharimalala and Arthur Randrianarivony
Flag-Major Index and Flag-Inversion Number on Colored Words and Wreath Product
In [Proc. Amer. Math. Soc. 19 (1968), 236-240],
Dominique Foata constructed a map \Phi, called
second fundamental transformation, exchanging the integer-valued
statistics inversion number "inv" and major index
"maj" on words whose letters are integers. Later, Foata and Han
introduced the flag-inversion number "finv" and extended
\Phi on signed words and permutations, showing that the flag
major index "fmaj" and "finv" were equidistributed. In this
paper we give an extension of \Phi to l-colored
words. Using this extension, we show that the bistatistics
(fmaj,desbis) and (finv,pcol) are equidistributed, where
"pcol" is the sum of color powers and
"desbis" is a new statistic derived from "des".
Received: August 7, 2009.
Accepted: January 4, 2010.
Final Version: January 11, 2010.
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