|
|||||
|
|
The limiting distribution of the coefficients of the  -Catalan numbers |
|
| Authors: | William Y C Chen Carol J Wang Larry X W Wang |
| Institution: | Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China ; Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China ; Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China |
| Abstract: | We show that the limiting distributions of the coefficients of the  -Catalan numbers and the generalized  -Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for small  , we conjecture that for sufficiently large  , the coefficients are unimodal and even log-concave except for a few terms of the head and tail. |
| Keywords: | Bernoulli number $q$-Catalan number unimodality log-concavity moment generating function |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 | |