Generalized Worpitzky Identities with Applications to Permutation Enumeration
Copyright © 1981 Elsevier.
The enumeration of permutations by inversions often leads to a q -analog of the usual generating function. In this paper, two generalizations of the Worpitzky identity for the Eulerian numbers are obtained and used to enumerate permutations by the descent number and the major index of their inverses. The resulting (t, q)-generating series do in fact generalize the q-series obtained when counting by inversions.
Don Rawlings. "Generalized Worpitzky Identities with Applications to Permutation Enumeration" European Journal of Combinatorics 2 (1981): 67-78.
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