# The Tutte polynomial

@article{Crapo1969TheTP,
title={The Tutte polynomial},
author={Henry Crapo},
journal={aequationes mathematicae},
year={1969},
volume={3},
pages={211-229}
}
• H. Crapo
• Published 1 October 1969
• Mathematics
• aequationes mathematicae
$q$-Matroids are defined on complemented modular support lattices. Minors of length 2 are of four types as in a "classical" matroid. Tutte polynomials $\tau(x,y)$ of matroids are calculated either by recursion over deletion/contraction of single elements, by an enumeration of bases with respect to internal/external activities, or by substitution $x \to (x-1),\; y \to (y-1)$ in their rank generating functions $\rho(x,y)$. The $q$-analogue of the passage from a Tutte polynomial to its…
224 Citations
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The main theorems represent Q_G as a quasi-specialization of the rank-generating polynomial $$S_G(x,y) of Oxley and Whittle, J Comb Theory Ser B 59:210–244, 1993, 1993) and show that \(Q_G$$ is likewise a generalized Tutte–Grothendieck invariant.

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