The algebraic combinatorics of snakes
Copyright policy )The algebraic combinatorics of snakes
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.
29 pages, Latex
Symmetric functions and generalizations, permutations, Snakes, snakes, Combinatorial aspects of groups and algebras, Theoretical Computer Science, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Noncommutative symmetric functions, Reflection and Coxeter groups (group-theoretic aspects), Computational Theory and Mathematics, generating functions, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, noncommutative symmetric functions, Combinatorics (math.CO), Euler numbers
Symmetric functions and generalizations, permutations, Snakes, snakes, Combinatorial aspects of groups and algebras, Theoretical Computer Science, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Noncommutative symmetric functions, Reflection and Coxeter groups (group-theoretic aspects), Computational Theory and Mathematics, generating functions, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, noncommutative symmetric functions, Combinatorics (math.CO), Euler numbers
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