On reid’s 3-simplicial matroid theorem

Abstract

In this paper we prove the following result of Ralph Reid (which was never published nor completely proved).

Theorem. Let M be a matroid coordinatizable (representable) over a prime field F. Then there is a 3-simplicial matroid M′ over F which is a series extension of M.

The proof we give is different from the original proof of Reid which uses techniques of algebraic topology. Our proof is constructive and uses elementary matrix operations.

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Cordovil, R. On reid’s 3-simplicial matroid theorem. Combinatorica 2, 135–141 (1982). https://doi.org/10.1007/BF02579311

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AMS Subject Classification (1980)

  • 05 B 35