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

Abstract. 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.

The following versions are available: