Positivity among P-partition generating functions
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908540214444032 |
|---|---|
| author | Lesnevich, Nathan R. T. McNamara, Peter R. W. |
| author_facet | Lesnevich, Nathan R. T. McNamara, Peter R. W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_10087 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Positivity among P-partition generating functions Lesnevich, Nathan R. T. McNamara, Peter R. W. Combinatorics Primary 05E05, Secondary 06A11, 06A07 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. |
| title | Positivity among P-partition generating functions |
| topic | Combinatorics Primary 05E05, Secondary 06A11, 06A07 |
| url | https://arxiv.org/abs/2006.10087 |