P-partition products and fundamental quasi-symmetric function positivity

Thomas Lam, Pavlo Pylyavskyy

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We show that certain differences of productsKQ ∧ R, θ KQ ∨ R, θ - KQ, θ KR, θ of P-partition generating functions are positive in the basis of fundamental quasi-symmetric functions Lα. This result interpolates between recent Schur positivity and monomial positivity results of the same flavor. We study the case of chains in detail, introducing certain "cell transfer" operations on compositions and a related "L-positivity" poset. We introduce and study quasi-symmetric functions called wave Schur functions and use them to establish, in the case of chains, that KQ ∧ R, θ KQ ∨ R, θ - KQ, θ KR, θ is itself equal to a single generating function KP, θ for a labeled poset (P, θ). In the course of our investigations we establish some factorization properties of the ring QSym of quasi-symmetric functions.

Original languageEnglish (US)
Pages (from-to)271-294
Number of pages24
JournalAdvances in Applied Mathematics
Volume40
Issue number3
DOIs
StatePublished - Mar 2008
Externally publishedYes

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: tfylam@math.harvard.edu (T. Lam), pasha@mit.edu (P. Pylyavskyy). 1 T.L. was partially supported by NSF DMS-0600677.

Fingerprint Dive into the research topics of 'P-partition products and fundamental quasi-symmetric function positivity'. Together they form a unique fingerprint.

Cite this