Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions
Combinatorics
2016-11-08 v1 Rings and Algebras
Abstract
In his work on P-partitions, Stembridge defined the algebra of peak functions Pi, which is both a subalgebra and a retraction of the algebra of quasi-symmetric functions. We show that Pi is closed under coproduct, and therefore a Hopf algebra, and describe the kernel of the retraction. Billey and Haiman, in their work on Schubert polynomials, also defined a new class of quasi-symmetric functions --- shifted quasi-symmetric functions --- and we show that Pi is strictly contained in the linear span Xi of shifted quasi-symmetric functions. We show that Xi is a coalgebra, and compute the rank of the n-th graded component.
Keywords
Cite
@article{arxiv.math/9904105,
title = {Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions},
author = {Nantel Bergeron and Stefan Mykytiuk and Frank Sottile and Stephanie van Willigenburg},
journal= {arXiv preprint arXiv:math/9904105},
year = {2016}
}
Comments
9 pages, 4 eps figures, uses epsf.sty. to be presented at FPSAC99 in Barcelona by second author