On the evaluation at (−ι,ι) of the Tutte polynomial of a binary matroid

@article{Pendavingh2012OnTE,
  title={On the evaluation at (−ι,ι) of the Tutte polynomial of a binary matroid},
  author={R. Pendavingh},
  journal={Journal of Algebraic Combinatorics},
  year={2012},
  volume={39},
  pages={141-152}
}
  • R. Pendavingh
  • Published 2012
  • Mathematics
  • Journal of Algebraic Combinatorics
Vertigan has shown that if M is a binary matroid, then |TM(−ι,ι)|, the modulus of the Tutte polynomial of M as evaluated in (−ι,ι), can be expressed in terms of the bicycle dimension of M. In this paper, we describe how the argument of the complex number TM(−ι,ι) depends on a certain $\mathbb{Z}/4\mathbb {Z}$-valued quadratic form that is canonically associated with M. We show how to evaluate TM(−ι,ι) in polynomial time, as well as the canonical tripartition of M and further related invariants. 
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References

SHOWING 1-10 OF 25 REFERENCES
On the evaluation at (j, j2) of the Tutte polynomial of a ternary matroid
  • 7
  • Highly Influential
  • PDF
On the computational complexity of the Jones and Tutte polynomials
  • 438
Tutte polynomials and bicycle dimension of ternary matroids
  • 15
  • Highly Influential
  • PDF
Bicycle Dimension and Special Points of the Tutte Polynomial
  • D. Vertigan
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1998
  • 33
  • Highly Influential
Computing Tutte Polynomials
  • 41
  • Highly Influential
  • PDF
Witt’s extension theorem for mod four valued quadratic forms
  • 14
  • PDF
On the Principal Edge Tripartition of a Graph
  • 92
  • Highly Influential
Skew partial fields, multilinear representations of matroids, and a matrix tree theorem
  • 17
  • PDF
Growth rates of minor-closed classes of matroids
  • 30
  • PDF
Practical graph isomorphism, II
  • 1,137
  • PDF
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