Published in Advances in Applied Mathematics, Volume 16, Issue 2, June 1, 1995, pages 206-218.
The definitive version is available at https://doi.org/10.1006/aama.1995.1010.
Based on two inversion formulas for enumerating words in the free monoid by adjacencies, we present a new approach to a class of permutation problems having Eulerian-type generating functions. We also show that a specialization of one of the inversion formulas gives Diekert's lifting to the free monoid of an inversion theorem due to Cartier and Foata.
1995 Academic Press, Inc.