Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials
We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a new result that the plethystic composition of a...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2015-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2483/pdf |
| _version_ | 1797270193161895936 |
|---|---|
| author | Masaki Watanabe |
| author_facet | Masaki Watanabe |
| author_sort | Masaki Watanabe |
| collection | DOAJ |
| description | We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a new result that the plethystic composition of a Schur function with a Schubertpolynomial is Schubert-positive. The present submission is an extended abstract on these results and the full versionof this work will be published elsewhere. |
| first_indexed | 2024-04-25T02:00:22Z |
| format | Article |
| id | doaj.art-2d9f15f893324263b7dafda5047ef08d |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:22Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-2d9f15f893324263b7dafda5047ef08d2024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.24832483Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomialsMasaki Watanabe0Graduate School of Mathematical Sciences[Tokyo]We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a new result that the plethystic composition of a Schur function with a Schubertpolynomial is Schubert-positive. The present submission is an extended abstract on these results and the full versionof this work will be published elsewhere.https://dmtcs.episciences.org/2483/pdfschubert functorskraśkiewicz-pragacz modulesschubert polynomialsschubert calculus[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Masaki Watanabe Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials Discrete Mathematics & Theoretical Computer Science schubert functors kraśkiewicz-pragacz modules schubert polynomials schubert calculus [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials |
| title_full | Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials |
| title_fullStr | Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials |
| title_full_unstemmed | Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials |
| title_short | Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials |
| title_sort | kraskiewicz pragacz modules and some positivity properties of schubert polynomials |
| topic | schubert functors kraśkiewicz-pragacz modules schubert polynomials schubert calculus [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2483/pdf |
| work_keys_str_mv | AT masakiwatanabe kraskiewiczpragaczmodulesandsomepositivitypropertiesofschubertpolynomials |