Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type

@article{Musiker2007CombinatorialIF,
  title={Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type},
  author={Gregg Musiker and James Gary Propp},
  journal={Electr. J. Comb.},
  year={2007},
  volume={14}
}
Fomin and Zelevinsky [6] show that a certain two-parameter family of rational recurrence relations, here called the (b, c) family, possesses the Laurentness property: for all b, c, each term of the (b, c) sequence can be expressed as a Laurent polynomial in the two initial terms. In the case where the positive integers b, c satisfy bc < 4, the recurrence is related to the root systems of finite-dimensional rank 2 Lie algebras; when bc > 4, the recurrence is related to Kac-Moody rank 2 Lie… CONTINUE READING
Highly Cited
This paper has 28 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
19 Citations
16 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 16 references

Positivity and canonical bases in rank 2 cluster algebras of finite and affine types

  • P. Sherman, A. Zelevinsky
  • Moscow Math. J. 4
  • 2004
Highly Influential
13 Excerpts

On the vector representations of induced matroids , Bull

  • B. Lindström
  • London Math . Soc .
  • 2004

Binomial determinants , paths , and hook length formulae

  • I. M. Gessel, G. Viennot
  • Ann . in Math .
  • 2003

Similar Papers

Loading similar papers…