Mathematics – Combinatorics
Scientific paper
2010-11-03
Mathematics
Combinatorics
22 pages
Scientific paper
Springer numbers are an analog of Euler numbers for the group of signed permutations. Arnol'd showed that they count some objects called snakes, that generalize alternating permutations. Hoffman established a link between Springer numbers, snakes, and some polynomials related with the successive derivatives of trigonometric functions. The goal of this article is to give further combinatorial properties of derivative polynomials, in terms of snakes and other objects: cycle-alternating permutations, weighted Dyck or Motzkin paths, increasing trees and forests. We obtain the generating functions, in terms of trigonometric functions for exponential ones and in terms of J-fractions for ordinary ones. We also define natural q-analogs, make a link with normal ordering problems and combinatorial theory of differential equations.
No associations
LandOfFree
Enumeration of snakes and cycle-alternating permutations 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 Enumeration of snakes and cycle-alternating permutations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enumeration of snakes and cycle-alternating permutations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-603691