TY - JOUR
T1 - Bijections related to statistics on words
AU - Greene, John
PY - 1988
Y1 - 1988
N2 - 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.
AB - 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.
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U2 - 10.1016/0012-365X(88)90038-6
DO - 10.1016/0012-365X(88)90038-6
M3 - Article
AN - SCOPUS:45549112131
SN - 0012-365X
VL - 68
SP - 15
EP - 29
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1
ER -