Year: 2026
Type: preprint
Abstract: 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 these four conjectures. The proofs are unified within a common algebraic framework: we interpret the Hankel determinants as Gram determinants and use a basis of shifted monic Chebyshev polynomials to reveal the finite-band structure of the associated Gram matrices.
Source: arXiv (Cornell University)
Authors: Liu, Feihu, Wang, Ying, Zhang, Zihao
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170057170