Narayana numbers and Schur-Szego composition
| dc.creator | Kostov, Vladimir | |
| dc.creator | Shapiro, Boris | |
| dc.date | 2008-04-07 | |
| dc.date.accessioned | 2026-07-07T09:30:49Z | |
| dc.date.available | 2026-07-07T09:30:49Z | |
| dc.description | In the present paper we find a new interpretation of Narayana polynomials N_n(x) which are the generating polynomials for the Narayana numbers N_{n,k} counting Dyck paths of length n and with exactly k peaks. Strangely enough Narayana polynomials also occur as limits as n->oo of the sequences of eigenpolynomials of the Schur-Szego composition map sending (n-1)-tuples of polynomials of the form (x+1)^{n-1}(x+a) to their Schur-Szego product, see below. As a corollary we obtain that every N_n(x) has all roots real and non-positive. Additionally, we present an explicit formula for the density and the distribution function of the asymptotic root-counting measure of the polynomial sequence {N_n(x)}. | |
| dc.description | 14 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0804.1028 | |
| dc.identifier | http://arxiv.org/abs/0804.1028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158246 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | 12D10 | |
| dc.title | Narayana numbers and Schur-Szego composition | |
| dc.type | text |