The algebraic combinatorics of snakes

10/2011; DOI: 10.1016/j.jcta.2012.05.002
Source: arXiv

ABSTRACT Snakes are analogues of alternating permutations defined for any Coxeter
group. We study these objects from the point of view of combinatorial Hopf
algebras, such as noncommutative symmetric functions and their generalizations.
The main purpose is to show that several properties of the generating functions
of snakes, such as differential equations or closed form as trigonometric
functions, can be lifted at the level of noncommutative symmetric functions or
free quasi-symmetric functions. The results take the form of algebraic
identities for type B noncommutative symmetric functions, noncommutative
supersymmetric functions and colored free quasi-symmetric functions.

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