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

Institutions

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
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Proofs of Okada's Conjectures 9.63 and 9.64 with constant-base-shift extensions (arXiv:2003.02112v2, Section 9.8.3)

Wenlin Zhang, Haobo Ma
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Proofs of Okada's Conjectures 9.63 and 9.64 with constant-base-shift extensions (arXiv:2003.02112v2, Section 9.8.3)

Wenlin Zhang, Haobo Ma
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
National University of Singapore (SG)
Advanced Combinatorial Mathematics
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon