Constructing Prime-field Planar Configurations
نویسنده
چکیده
An infinite class of planar configurations is constructed with distinct prime-field characteristic sets (i.e., configurations represented over a finite set of prime fields but over fields of no other characteristic). It is shown that if p is sufficiently large, then every subset of k primes between p and f(p, k) forms such a set (where f(p, k) = 2[(f-Ak3//2)Bk3/21 for constants A and B). In particular, for every positive integer k, there exist infinitely many planar matroid configurations Ci, k with IXpf(Ci k)I = k (where Xpf(C) denotes the prime-field characteristic set of C). We also give a result concerning cofinite prime-field characteristic sets.
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