On the ideals of equivariant tree models

Mathematische Annalen

Volumn 344, Issue 3, 2009, Pages 619-644

  Draisma, Jan ^a,b   Kuttler, Jochen ^c  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b CWI   (Netherlands)

^c UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67349239392     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-008-0320-6     Document Type: Article

References (17)

1. E.S. Allman J.A. Rhodes 2008 Phylogenetic ideals and varieties for the general Markov model Adv. Appl. Math. 40 2 127 148
2. W. Buczyńska J.A. Wiśniewski 2007 On geometry of binary symmetric models of phylogenetic trees J. Eur. Math. Soc. 9 3 609 635
3. Casanellas, M., Fernández-Sánchez, J.: The geometry of the Kimura 3-parameter model. Adv. Appl. Math. (2007, to appear). Preprint available from http://arxiv.org/abs/math/0702834
4. Casanellas M., Sullivant S.: The strand symmetric model. In: Algebraic Statistics for Computational Biology. Cambridge University Press, Cambridge (2005)
5. Derksen H., Kemper G.: Computational Invariant Theory, vol. 130 of Encyclopaedia of Mathematical Sciences. Springer, Berlin (2002)
6. H. Diaconis B. Sturmfels 1998 Algebraic algorithms for sampling from conditional distributions Ann. Stat. 26 1 363 397 (Pubitemid 128377105)
7. Eriksson, N., Ranestad, K., Sturmfels, B., Sullivant, S.: Phylogenetic algebraic geometry. In: Projective varieties with unexpected properties, pp. 237-255. Walter de Gruyter GmbH & Co. KG (2005)
8. S.N. Evans T.P. Speed 1993 Invariants of some probability models used in phylogenetic inference Ann. Statist. 21 1 355 377
9. L.D. Garcia M. Stillman B. Sturmfels 2005 Algebraic geometry of Bayesian networks J. Symb. Comput. 39 3-4 331 355 (Pubitemid 40373617)
10. Goodman R., Wallach N.R.: Representations and Invariants of the Classical Groups. Cambridge University Press, London (1998)
11. Hartshorne R.: Algebraic Geometry. Springer, New York (1977)
12. Kraft, H., Procesi, C.: A Primer in Invariant Theory (unpublished). Text available from http://www.math.unibas.ch/~kraft/Papers/KP-Primer.pdf
13. J.M. Landsberg L. Manivel 2004 On the ideals of secant varieties of Segre varieties Found. Comput. Math. 4 4 397 422 (Pubitemid 40002963)
14. J.M. Landsberg J. Weyman 2007 On the ideals and singularities of secant varieties of Segre varieties Bull. Lond. Math. Soc. 39 4 685 697
15. Pachter, L., Sturmfels, B. (eds): Algebraic Statistics for Computational Biology. Cambridge University Press, Cambridge (2005)
16. B. Sturmfels S. Sullivant 2005 Toric ideals of phylogenetic invariants J. Comput. Biol. 12 204 228 (Pubitemid 40444588)
17. Weyl H.: The Classical Groups, their Invariants and Representations. Princeton University Press, Princeton, NJ (1939)