Restricted permutations, continued fractions, and Chebyshev polynomials
| dc.creator | Mansour, T. | |
| dc.creator | Vainshtein, A. | |
| dc.date | 1999-12-06 | |
| dc.date | 2000-03-14 | |
| dc.date.accessioned | 2026-07-07T05:32:10Z | |
| dc.date.available | 2026-07-07T05:32:10Z | |
| dc.description | Let f_n^r(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12... k, and let F_r(x;k) and F(x,y;k) be the generating functions defined by $F_r(x;k)=\sum_{n\gs0} f_n^r(k)x^n$ and $F(x,y;k)=\sum_{r\gs0}F_r(x;k)y^r$. We find an explcit expression for F(x,y;k) in the form of a continued fraction. This allows us to express F_r(x;k) for $1\ls r\ls k$ via Chebyshev polynomials of the second kind. | |
| dc.identifier | https://arxiv.org/abs/math/9912052 | |
| dc.identifier | http://arxiv.org/abs/math/9912052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79559 | |
| dc.subject | Combinatorics | |
| dc.title | Restricted permutations, continued fractions, and Chebyshev polynomials | |
| dc.type | text |