5 papers
Hankel Transform and Somos-4 Sequences
Feihu Liu, Ying Wang, Zihao Zhang
An Somos- sequence is defined by the recurrence (), with suitable initial values, where and are constant p…
Proof of Barry's Four Hankel Determinant Conjectures
Feihu Liu, Ying Wang, Zihao Zhang
Barry introduced a central transform of integer sequences and proposed four conjectures concerning the Hankel transforms of central transform of four rational families. We prove th…
Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results
Feihu Liu, Ying Wang, Yingrui Zhang +1
Cigler considered certain shifted Hankel determinants of convolution powers of Catalan numbers and conjectured identities for these determinants. Recently, Fulmek gave a bijective…
Hankel Determinants for a Class of Weighted Lattice Paths
Ying Wang, Zihao Zhang
In this paper, our primary goal is to calculate the Hankel determinants for a class of lattice paths, which are distinguished by the step set consisting of \(\{(1,0), (2,0), (k-1,1…
A sufficient condition for Somos Hankel determinants
Ying Wang, Zihao Zhang
By using Sulanke-Xin continued fractions method, Xin proposed a recursion system to solve the Somos 4 Hankel determinant conjecture. We find Xin's recursion system indeed give a su…