A note on three types of quasisymmetric functions

Details A note on three types of quasisymmetric functions A note on three types of quasisymmetric functions

2005-08-08

arxiv.org/abs/math/0508149v1

Mathematics

Combinatorics

10 pages

Scientific paper

In the context of generating functions for $P$-partitions, we revisit three flavors of quasisymmetric functions: Gessel's quasisymmetric functions, Chow's type B quasisymmetric functions, and Poirier's signed quasisymmetric functions. In each case we use the inner coproduct to give a combinatorial description (counting pairs of permutations) to the multiplication in: Solomon's type A descent algebra, Solomon's type B descent algebra, and the Mantaci-Reutenauer algebra, respectively. The presentation is brief and elementary, our main results coming as consequences of $P$-partition theorems already in the literature.

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