Shifted quasi-symmetric functions and the Hopf algebra of peak functions Academic Article

abstract

• In his work on P-partitions, Stembridge defined the algebra of peak functions II, which is both a subalgebra and a retraction of the algebra of quasi-symmetric functions. We show that II 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 II is strictly contained in the linear span S of shifted quasi-symmetric functions. We show that E is a coalgebra, and compute the rank of the nth graded component. 2002 Elsevier Science B.V. All rights reserved.

authors

• Sottile, Frank

published proceedings

• Discrete Mathematics

author list (cited authors)

• Bergeron, N., Mykytiuk, S., Sottile, F., & van Willigenburg, S.

citation count

• 18

complete list of authors

• Bergeron, Nantel||Mykytiuk, Stefan||Sottile, Frank||van Willigenburg, Stephanie

publication date

• January 2002

publisher

• Elsevier  Publisher

published in

• Discrete Mathematics  Journal

Digital Object Identifier (DOI)

• 10.1016/s0012-365x(01)00251-5

start page

• 57

end page

• 66

volume

• 246

issue

• 1-3

URL

• http://dx.doi.org/10.1016/s0012-365x(01)00251-5