On a Claimed Upper Bound for Partial Desarguesian Parallelisms
Year: 2026
Type: preprint
Abstract: Johnson claimed an upper bound for partial Desarguesian t-parallelisms when t is prime. For every prime power q, odd prime t at least 3, and z at least 2, this correction note proves that the Zhang--Zhou GL(zt,q)-orbit lower bound strictly exceeds Johnson's claimed upper bound. The note verifies that the orbit witnesses satisfy the required individual Desarguesianity condition, explains why an unresolved common-subplane step is fatal to the published theorem, and supplies a compact exact certificate of 18 pairwise disjoint Desarguesian 3-spreads in V(6,2). Earlier work on PG(5,2) already implies a complete finite counterexample, so the first counterexample is not claimed. Status: Public Beta v0.1; internally verified correction note; external mathematical review pending.
Author: Carptopus
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204242029
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