A half-descent of an alternating permutation π is an event that π2i>π2i+2, which is defined and studied in Huber and Yee (2010) . The notion of half-descents is generalized to mth descents. Bivariate generating functions for permutations classified according to the numbers of mth descents and inversions are given. Connections to the results on half-descents and alternating permutations are indicated. It is also shown how to specialize the presented results to obtain some other previous work on permutations.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics