Triple O'Nan conjecture for non-classical unitals

Let qq be a prime power and let U{\mathcal U} be a non-classical unital in PG(2,q2){\textup{PG}}(2,q^2). A Triple O'Nan configuration is a set of six distinct lines pairwise intersecting in exactly seven points of the unital and containing three distinct O'Nan configurations. Triple O'Nan conjecture. Every non-classical unital U{\mathcal U} in PG(2,q2){\textup{PG}}(2,q^2) contains a Triple O'Nan configuration if q>5q>5. The paper proves the existence of such configurations for Buekenhout-Metz unitals of odd order, while the stated conjecture concerns all non-classical unitals in PG(2,q2){\textup{PG}}(2,q^2); the source gives no resolution status.

Sources & referencesView supporting material

Primary source

Wen-Ai Jackson and Peter Wild, “Triple O'Nan Configurations in Buekenhout-Metz Unitals of Odd Order”, arXiv:2403.05027 (2024).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.