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Aart Blokhuis is a mathematician working in finite geometry and combinatorics. With G. Eric Moorhouse, he calculated characteristic-$p$ rank formulas for the point-hyperplane incidence matrix of a set system associated with finite quadrics, and applied them to bounds and nonexistence results for ovoids.^[ref]

The coefficient field is essential to this method. For an elementary illustration, the integer matrix $\left(\begin{array}{cc}1& 1\\ 1& -1\end{array}\right)$ has rank two over $\mathbb{Q}$, but rank one over ${\mathbb{F}}_2$. Relations revealed by reduction modulo a prime number can therefore constrain configurations that a characteristic-zero calculation misses. His paper on few-distance sets provides another example of turning geometric restrictions into algebraic counting bounds.^[ref]

G. Eric Moorhouse is a mathematician whose work includes finite geometry, incidence structures and coding theory. His author homepage identifies him as Eric Moorhouse and records a University of Wyoming faculty appointment beginning in 1989.^[ref]

With Aart Blokhuis, he computed characteristic-$p$ rank formulas for the point-hyperplane incidence matrix of a set system in finite orthogonal geometries. Their calculations yield bounds on ovoids and rule out their existence in several families.^[ref] The link is that an incidence matrix converts containment statements into vectors over a finite field. A proposed geometric configuration must satisfy the resulting linear constraints, so linear algebra can prove that the configuration cannot exist. This makes incidence ranks useful structural information, rather than merely a numerical summary of a matrix.

By Aart Blokhuis and G. Eric Moorhouse.

Verified locator: 1995 paper, section 4, concluding discussion of ovoids of PG(3,q); manuscript page 23.