P-partition products and fundamental quasi-symmetric function positivity
| dc.creator | Lam, Thomas | |
| dc.creator | Pylyavskyy, Pavlo | |
| dc.date | 2006-09-08 | |
| dc.date.accessioned | 2026-07-07T07:24:40Z | |
| dc.date.available | 2026-07-07T07:24:40Z | |
| dc.description | We show that certain differences of products of $P$-partition generating functions are positive in the basis of fundamental quasi-symmetric functions L_α. 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 an interesting 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 the difference of products we study is itself equal to a single generating function K_{P,θ} for a labeled poset (P,θ). In the course of our investigations we establish some factorization properties of the ring of quasisymmetric functions. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609249 | |
| dc.identifier | http://arxiv.org/abs/math/0609249 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116446 | |
| dc.subject | Combinatorics | |
| dc.subject | 06A07; 05A20 | |
| dc.title | P-partition products and fundamental quasi-symmetric function positivity | |
| dc.type | text |