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Hilbert Polynomial of the Kimura 3-Parameter Model .

Journal Name:

  • Journal of Algebraic Statistics

Publication Year:

  • 2012

Key Words:

Author NameUniversity of Author

AMS Codes:

Abstract (2. Language): 
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.
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  • English

REFERENCES

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