A conjecture based on Somos-4 sequence and its extension
A conjecture based on Somos-4 sequence and its extension
复制标题
DOI：
10.1016/j.laa.2012.01.016
复制
发表时间：
2012-06
影响因子：
1.1
通讯作者：
Xiang-Ke Chang;Xing-Biao Hu
中科院分区：
文献类型：
--
作者：
Xiang-Ke Chang;Xing-Biao Hu
In two recent papers by Barry (2010) [29] and (2011) [30], it is conjectured that Somos-4 admits a solution expressed in terms of Hankel determinant with its elements satisfying a convolution recursion relation. In this paper, Barry’s conjecture on Somos-4 is firstly confirmed. Actually, we present a more generalized result. The proof is mainly based on new findings on properties for so-called Block–Hankel determinants. The method can also be used to prove another conjecture proposed by Michael Somos, which has been solved by Guoce Xin.
