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Bicycle Dimension and Special Points of the Tutte Polynomial

✍ Scribed by Dirk Vertigan

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 308 KB
Volume: 74
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1860

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✦ Synopsis

For each pair of algebraic numbers (x, y) and each field F, the complexity of computing the Tutte polynomial T(M; x, y) of a matroid M representable over F is determined. This computation is found to be *P-complete except when (x&1)( y&1)=1 or when |F| divides (x&1)( y&1) and (x, y) is one of the seven points (0, &1), (&1, 0), (i, &i), (&i, i), ( j, j 2 ), ( j 2 , j ) or (&1, &1), where j=e 2?iÂ3 . Expressions are given for the Tutte polynomial in the exceptional cases. These expressions involve the bicycle dimension of M over F. A related result determines when this bicycle dimension is well defined.

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