PreprintCC BY 4.0arXiv
Proof of Barry's Four Hankel Determinant Conjectures
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.
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BibTeX
@misc{liu2026proof,
title = {{Proof of Barry's Four Hankel Determinant Conjectures}},
author = {Feihu Liu and Ying Wang and Zihao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.18644},
eprint = {2607.18644},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18644},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Proof of Barry's Four Hankel Determinant Conjectures
AU - Feihu Liu
AU - Ying Wang
AU - Zihao Zhang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2607.18644
UR - https://arxiv.org/abs/2607.18644
AB - 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.
ER -