We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generating functions of Stanley's (P,ω)-partitions.
|Original language||English (US)|
|Number of pages||16|
|Journal||Journal of Algebraic Combinatorics|
|State||Published - Sep 2007|
Bibliographical noteFunding Information:
T.L. was supported in part by NSF DMS-0600677.
- Monomial positivity
- Symmetric functions