Proofs of Okada's Conjectures 9.63 and 9.64 with constant-base-shift extensions (arXiv:2003.02112v2, Section 9.8.3)
We prove Conjectures 9.63 and 9.64 in Section 9.8.3 of Okada's arXiv:2003.02112v2. At unit weights and degree shift zero, every natural width at least three gives a non-almost-palindromic determinant. At width two, almost palindromicity holds exactly when min(a2-a1,b2-b1)=1, giving proportion (lambda-2)(lambda-3)/(lambda(lambda+1)) at b2=lambda>=2. These conclusions hold for every constant positive integral base shift. An infinite family extends the width-two counterexample in Example 9.65. Conjecture 9.66, whose width is at least three, is proved on degree-shift slices e=0,1,G-1,G and at e=G/2 when G is even, where G is the direct-minus-reversed degree gap. The remaining degree shifts are not covered.
Authors
- Wenlin Zhang (ORCID: https://orcid.org/0009-0005-2414-7968)
- Haobo Ma
Institutions
- National University of Singapore (SG)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.5281/zenodo.23927423
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- preprint