Séminaire Lotharingien de Combinatoire, B54a (2006), 20 pp.

Dominique Foata and Guo-Niu Han

Signed Words and Permutations, III: the MacMahon Verfahren

Abstract. The MacMahon Verfahren is fully exploited to derive a five-variable generating polynomial over signed permutations, where the parameters are: "neg" (number of negative values), "fdes" (flag descent number), "fmaj" (flag major index), "ifdes" and "ifmaj" (fdes and fmaj for the inverse permutation); then a three-variable generating polynomial over signed words with given letter multiplicities, where the parameters are "neg", "fmaj", and "fdes".

Received: May 27, 2005. Accepted: January 1, 2006. Final Version: January 3, 2006.

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