We introduce and study three new statistics on the even-signed permutation group D_n. We show that two of these are Mahonian, i.e., are equidistributed with length, and that a pair of them gives a generalization of Carlitz’s identity on the Euler-Mahonian distribution of the descent number and major index over S_n.
Biagioli R (2003). Major and descent statistics for the even-signed permutation group. ADVANCES IN APPLIED MATHEMATICS, 31, 163-179 [10.1016/S0196-8858(02)00561-4].
Major and descent statistics for the even-signed permutation group
Biagioli R
2003
Abstract
We introduce and study three new statistics on the even-signed permutation group D_n. We show that two of these are Mahonian, i.e., are equidistributed with length, and that a pair of them gives a generalization of Carlitz’s identity on the Euler-Mahonian distribution of the descent number and major index over S_n.File in questo prodotto:
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