Breakthrough Tracker record
Claimed counterexamples to the Duval–Reiner majorization conjecture
Huang reports strict counterexamples to the majorization assertion for every index r at least 5 in some uniformity and for every uniformity q at least 3 at some index. The paper separately proves the universal second partial-sum inequality and classifies its equality cases.
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- Stable ID
math-duval-reiner-counterexamples-2026- Revision
math-duval-reiner-counterexamples-2026.v1- Field
- Mathematics · Algebraic combinatorics and spectral theory
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Preprint counterexamples; verification pending
- Last checked
AI role
No substantive AI role was disclosed in the inspected manuscript.
Record details
- Problem or result
- Duval–Reiner majorization assertion for simplicial up-Laplacian spectra
- Authors
- Jing Huang
- Institutions
- Guangzhou University
- Result date
- Preprint submitted July 22, 2026
Why it matters
The result would delimit how far graph Laplacian majorization extends to higher-dimensional uniform simplicial families.
Limits
The counterexamples appear in a same-day version-one preprint. No independent recomputation, specialist assessment or journal review was located by the maintenance cutoff.
Sources
- Primary: Jing Huang, The Duval–Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality
- Independent: Earlier partial result on the second partial-sum case
Correction and revision history
- 2026-07-22 — Added as a version-one preprint disproof claim pending independent verification.
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