Matroid Correlation
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proved exact · solid curve

Huh–Schröter–Wang finite-field spikes

A rank-5 family over \(\operatorname{GF}(p)\) whose correlation constant is exactly \(\frac{8}{7}\) for every displayed prime \(p\).

parameter

prime \(p\)

supremum

supremum 8/7 — attained by every member

discovered by

June Huh, Benjamin Schröter, Botong Wang

discovery date

June 2018

Construction

For each prime \(p\), Huh, Schröter, and Wang define the finite-field spike \(M_p^5\) over \(\operatorname{GF}(p)\): the tip \(e_1\), the vector \(e_2+\cdots+e_5\), and \(k\,e_1+e_m\) for \(m=2,\ldots,5\) and \(k\in\operatorname{GF}(p)\). It has rank 5 and \(4p+2\) elements, so the curve consists of genuine finite matroids at the admissible prime parameters. The same construction works verbatim over any finite field; this site also verified the member at \(q=4\).

What the curve shows

The full maximum over eligible element pairs is \(\frac{8}{7}\) for every member, so this is a horizontal solid curve: the value is attained on the nose by each finite member, not merely in a limit.

Proof status

The exact family value is proved in the cited paper. This site independently reconstructed every basis and recomputed the full maximum for the members over GF(2), GF(3), GF(4), GF(5), and GF(7). Full proof on the mathematics page →

AI disclosure

No AI use is reported in the cited discovery record.

Plotted members

Mₚ⁵ (10 plotted members)