Bijections related to statistics on words

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Abstract

Combinatorial proofs of the identities ∑ w∈MqInv(w)= n1+n2+⋯+nkn1,n2,⋯,n1= ∑ w∈Mqz(w) are given and bijections are constructed between the sets {w ∈ M | Inv(w) = m}, {w ∈ M | Maj(w) = m}, {w ∈ M | Z(w) = m}, where M is the collection of all multiset permutations with n11's, n22's,...,nkk's, Inv(w) is the inversion number of w, Maj(w) is its major index and Z(w) is the z-index of w.

Original languageEnglish (US)
Pages (from-to)15-29
Number of pages15
JournalDiscrete Mathematics
Volume68
Issue number1
DOIs
StatePublished - 1988

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