Constructing prime-field planar configurations

Author:
Gary Gordon

Journal:
Proc. Amer. Math. Soc. **91** (1984), 492-502

MSC:
Primary 05B35; Secondary 51D20

DOI:
https://doi.org/10.1090/S0002-9939-1984-0744655-1

MathSciNet review:
744655

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Abstract: 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 is sufficiently large, then every subset of primes between and forms such a set (where for constants and ). In particular, for every positive integer , there exist infinitely many planar matroid configurations with (where denotes the prime-field characteristic set of ). We also give a result concerning cofinite prime-field characteristic sets.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0744655-1

Keywords:
Matroid configuration,
characteristic set,
prime-field characteristic set

Article copyright:
© Copyright 1984
American Mathematical Society