Log-concavity and LC-positivity
| dc.creator | Wang, Yi | |
| dc.creator | Yeh, Yeong-Nan | |
| dc.date | 2005-04-08 | |
| dc.date | 2006-11-27 | |
| dc.date.accessioned | 2026-07-07T06:39:44Z | |
| dc.date.available | 2026-07-07T06:39:44Z | |
| dc.description | A triangle $\{a(n,k)\}_{0\le k\le n}$ of nonnegative numbers is LC-positive if for each $r$, the sequence of polynomials $\sum_{k=r}^{n}a(n,k)q^k$ is $q$-log-concave. It is double LC-positive if both triangles $\{a(n,k)\}$ and $\{a(n,n-k)\}$ are LC-positive. We show that if $\{a(n,k)\}$ is LC-positive then the log-concavity of the sequence $\{x_k\}$ implies that of the sequence $\{z_n\}$ defined by $z_n=\sum_{k=0}^{n}a(n,k)x_k$, and if $\{a(n,k)\}$ is double LC-positive then the log-concavity of sequences $\{x_k\}$ and $\{y_k\}$ implies that of the sequence $\{z_n\}$ defined by $z_n=\sum_{k=0}^{n}a(n,k)x_ky_{n-k}$. Examples of double LC-positive triangles include the constant triangle and the Pascal triangle. We also give a generalization of a result of Liggett that is used to prove a conjecture of Pemantle on characteristics of negative dependence. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504164 | |
| dc.identifier | http://arxiv.org/abs/math/0504164 | |
| dc.identifier | J. Combin. Theory, Ser. A 114 (2007) 195--210 | |
| dc.identifier | doi:10.1016/j.jcta.2006.02.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101188 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A20; 15A04 | |
| dc.title | Log-concavity and LC-positivity | |
| dc.type | text |