Mathematics – Combinatorics
Scientific paper
2011-07-09
Mathematics
Combinatorics
Scientific paper
We show that the size of the intersection of a Hermitian variety in $\PG(n,q^2)$, and any set satisfying an $r$-dimensional-subspace intersection property, is congruent to 1 modulo a power of $p$. In particular, in the case where $n=2$, if the two sets are a Hermitian unital and any other unital, the size of the intersection is congruent to 1 modulo $\sqrt q$ or modulo $\sqrt{pq}$. If the second unital is a Buekenhout-Metz unital, we show that the size is congruent to 1 modulo $q$.
Chandler David B.
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