2005/08/08 by T. Kyle Petersen, Petersen, T. Kyle
Mathematics · #05E99 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E99
paper · pdf · doi:10.48550/arxiv.math/0508149
10 pages
arxiv created 2005/08/08 · arxiv updated 2009/12/01
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.