T. Bisztriczky - A Signature Theorem for uniform oriented matroids

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T. Bisztriczky - A Signature Theorem for uniform oriented matroids

T. BISZTRICZKY, Department of Mathematics, University of Calgary, Calgary, Alberta T2N 2N4, Canada

A Signature Theorem for uniform oriented matroids

Let M be an uniform oriented matroid over a set E of n elements $e(1), e(2),\dots,e(n)$ endowed with the linear order $e(1)<e(2)<\cdots<e(n)$ . We say that e(i) and e(i+1) are successive elements of E. The Signature Lemma of Cordovil and Duchet states that if for any circuit C, (*) successive elements of Ethat are in C have alternating signs in C, then M is alternating with respect to the linear order. In the Signature Theorem, the condition (*) is weakened.