Publication Date
1-16-2022
Description
We seek simple conditions on a pair of labeled posets that determine when the difference of their (P,ω)-partition enumerators is F-positive, i.e., positive in Gessel's fundamental basis. This is a quasisymmetric analogue of the extensively studied problem of finding conditions on a pair of skew shapes that determine when the difference of their skew Schur functions is Schur-positive. We determine necessary conditions and separate sufficient conditions for F-positivity, and show that a broad operation for combining posets preserves positivity properties. We conclude with classes of posets for which we have conditions that are both necessary and sufficient.
Journal
Annals of Combinatorics
Volume
26
Issue
1
First Page
171
Last Page
204
Department
Mathematics
Link to Published Version
https://link.springer.com/article/10.1007/s00026-021-00563-2
DOI
https://doi.org/10.1007/s00026-021-00563-2
Recommended Citation
Lesnevich, Nathan R. T. and McNamara, Peter R. W.. "Positivity among P-partition generating functions." (2022) : 171-204.