Alternating permutations and the mth descents

作者：Kursungoez Kagan; Yee Ae Ja^*

来源：Discrete Mathematics, 2011, 311(22): 2610-2622.

DOI：10.1016/j.disc.2011.08.005

• Permutations
• Inversions
• Descents
• mth descents
• q-Euler numbers
• q-analogs

A half-descent of an alternating permutation pi is an event that pi(2i) > pi(2i+2), which is defined and studied in Huber and Yee (2010) [18]. 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.

• 出版日期2011-11-28