Schur Positivity and the $q$-Log-convexity of the Narayana Polynomials
| dc.creator | Chen, William Y. C. | |
| dc.creator | Wang, Larry X. W. | |
| dc.creator | Yang, Arthur L. B. | |
| dc.date | 2008-06-10 | |
| dc.date.accessioned | 2026-07-07T09:43:34Z | |
| dc.date.available | 2026-07-07T09:43:34Z | |
| dc.description | Using Schur positivity and the principal specialization of Schur functions, we provide a proof of a recent conjecture of Liu and Wang on the $q$-log-convexity of the Narayana polynomials, and a proof of the second conjecture that the Narayana transformation preserves the log-convexity. Based on a formula of Bränd$\mathrm{\acute{e}}$n which expresses the $q$-Narayana numbers as the specializations of Schur functions, we derive several symmetric function identities using the Littlewood-Richardson rule for the product of Schur functions, and obtain the strong $q$-log-convexity of the Narayana polynomials and the strong $q$-log-concavity of the $q$-Narayana numbers. | |
| dc.description | 38 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0806.1561 | |
| dc.identifier | http://arxiv.org/abs/0806.1561 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162604 | |
| dc.subject | Combinatorics | |
| dc.title | Schur Positivity and the $q$-Log-convexity of the Narayana Polynomials | |
| dc.type | text |