The Tutte polynomial

  title={The Tutte polynomial},
  author={Henry Crapo},
  journal={aequationes mathematicae},
  • 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… 
The Tutte q-Polynomial
$q$-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
Interpretations of the Tutte and characteristic polynomials of matroids
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  • Mathematics
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  • 2019
We study interpretations of the Tutte and characteristic polynomials of matroids. If M is a matroid with rank function r whose ground set E is given with a linear ordering <, then $$X\subseteq E$$ X
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Tutte Polynomial Activities.
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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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Lectures on matroids
Lattice Differentials
  • and the Theory of Combinatorial Independence, Research Reports, Northeastern University
  • 1964
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