PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 9 | 1577-1592
Tytuł artykułu

On the graph labellings arising from phylogenetics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
Twórcy
autor
Bibliografia
  • [1] Bosma W., Cannon J., Playoust C., The Magma algebra system. I. The user language, In: Computational Algebra and Number Theory, London, August 23–27, 1993, J. Symbolic Comput., 1997, 24(3–4), 235–265
  • [2] Brown G., Buczyński J., Kasprzyk A., Chapter: Convex polytopes and polyhedra, The Magma Handbook, University of Sydney, available at http://magma.maths.usyd.edu.au/
  • [3] Buczyńska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460 http://dx.doi.org/10.1007/s10801-011-0308-2
  • [4] Buczyńska W., Wiśniewski J.A., On geometry of binary symmetric models of phylogenetic trees, J. Eur. Math. Soc. (JEMS), 2007, 9(3), 609–635 http://dx.doi.org/10.4171/JEMS/90
  • [5] Donten-Bury M., Michałek M., Phylogenetic invariants for group-based models, J. Algebr. Stat., 2012, 3(1), 44–63
  • [6] Faltings G., A proof for the Verlinde formula, J. Algebraic Geom., 1994, 3(2), 347–374
  • [7] Jeffrey L.C., Weitsman J., Bohr-Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula, Comm. Math. Phys., 1992, 150(3), 593–630 http://dx.doi.org/10.1007/BF02096964
  • [8] Kubjas K., Hilbert polynomial of the Kimura 3-parameter model, J. Algebr. Stat., 2012, 3(1), 64–69
  • [9] Manon C., Coordinate rings for the moduli stack of SL2(ℂ) quasi-parabolic principal bundles on a curve and toric fiber products, J. Algebra, 2012, 365, 163–183 http://dx.doi.org/10.1016/j.jalgebra.2012.05.007
  • [10] Manon C., The algebra of conformal blocks, preprint available at http://arxiv.org/abs/0910.0577v3
  • [11] Michałek M. Geometry of phylogenetic group-based models, J. Algebra, 2011, 339, 339–356 http://dx.doi.org/10.1016/j.jalgebra.2011.05.016
  • [12] Michałek M., Toric geometry of the 3-Kimura model for any tree, Adv. Geom. (in press), preprint available at http://arxiv.org/abs/1102.4733v4
  • [13] Neyman J., Molecular studies in evolution: a source of novel statistical problems, In: Statistical Decision Theory and Related Topics, Academic Press, New York, 1971, 1–27
  • [14] Pachter L., Sturmfels B., Statistics, In: Algebraic Statistics for Computational Biology, Cambridge University Press, New York, 2005, 3–42 http://dx.doi.org/10.1017/CBO9780511610684.004
  • [15] Sturmfels B., Sullivant S., Toric ideals of phylogenetic invariants, Journal of Computational Biology, 2005, 12(2), 204–228 http://dx.doi.org/10.1089/cmb.2005.12.204
  • [16] Sturmfels B., Velasco M., Blow-ups of ℙn−3 at n points and spinor varieties, J. Commut. Algebra, 2010, 2(2), 223–244 http://dx.doi.org/10.1216/JCA-2010-2-2-223
  • [17] Sturmfels B., Xu Z., Sagbi basis and Cox-Nagata rings, J. Eur. Math. Soc. (JEMS), 2010, 12(2), 429–459 http://dx.doi.org/10.4171/JEMS/204
  • [18] Verlinde E., Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B, 1988, 300(3), 360–376 http://dx.doi.org/10.1016/0550-3213(88)90603-7
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0263-3
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.