Hilbert Polynomial of the Kimura 3-Parameter Model

  • Kaie Kubjas Author University: Freie Universität Berlin Author Department: Institut für Mathematik
Keywords: Kimura 3-parameter model, Hilbert polynomial, toric fiber products, lattice polytopes

Abstract

In [2] Buczy´nska and Wi´sniewski showed that the Hilbert polynomial of the algebraic
variety associated to the Jukes-Cantor binary model on a trivalent tree depends only on the number
of leaves of the tree and not on its shape. We ask if this can be generalized to other group-based
models. The Jukes-Cantor binary model has Z2 as the underlying group. We consider the Kimura
3-parameter model with Z2 × Z2 as the underlying group. We show that the generalization of the
statement about the Hilbert polynomials to the Kimura 3-parameter model is not possible as the
Hilbert polynomial depends on the shape of a trivalent tree.

References

Published Year: 2012
Volume: 3
Number: 1
Page Numbers: 64-69
Published
2012-04-30