Mathematics – Combinatorics
Scientific paper
2002-06-17
Mathematics
Combinatorics
22 pages
Scientific paper
In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding involutions and Dyck word prefixes of same length. Extending this bijection to bilateral words allows to determine more parameters; in particular, we consider the number of inversions and rises of the involutions onto the words. This is the starting point for considering two different directions: even/odd involutions and statistics of some generalized patterns. Thus we first study generating functions for the number of even or odd involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern $\tau$ on k letters. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. Next, we consider other statistics on 132-avoiding involutions by counting an occurrences of some generalized patterns, related to the enumeration according to the number of rises.
Guibert Olivier
Mansour Toufik
No associations
LandOfFree
Some statistics on restricted 132 involutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some statistics on restricted 132 involutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some statistics on restricted 132 involutions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-366866