Edge coloring models and reflection positivity
HTML articles powered by AMS MathViewer
- by Balázs Szegedy;
- J. Amer. Math. Soc. 20 (2007), 969-988
- DOI: https://doi.org/10.1090/S0894-0347-07-00568-1
- Published electronically: May 31, 2007
- PDF | Request permission
Abstract:
Solving a conjecture of M. H. Freedman, L. Lovász and A. Schrijver, we prove that a graph parameter is edge reflection positive and multiplicative if and only if it can be represented by an edge coloring model.References
- Michael Atiyah, The geometry and physics of knots, Lezioni Lincee. [Lincei Lectures], Cambridge University Press, Cambridge, 1990. MR 1078014, DOI 10.1017/CBO9780511623868
- Jacek Bochnak, Michel Coste, and Marie-Françoise Roy, Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 36, Springer-Verlag, Berlin, 1998. Translated from the 1987 French original; Revised by the authors. MR 1659509, DOI 10.1007/978-3-662-03718-8
- Michael H. Freedman, Alexei Kitaev, Chetan Nayak, Johannes K. Slingerland, Kevin Walker, and Zhenghan Wang, Universal manifold pairings and positivity, Geom. Topol. 9 (2005), 2303–2317. MR 2209373, DOI 10.2140/gt.2005.9.2303
- Michael Freedman, László Lovász, and Alexander Schrijver, Reflection positivity, rank connectivity, and homomorphism of graphs, J. Amer. Math. Soc. 20 (2007), no. 1, 37–51. MR 2257396, DOI 10.1090/S0894-0347-06-00529-7 FLSPPersonal communication with M.H. Freedman, L. Lovász, A. Schrijver.
- László Lovász, The rank of connection matrices and the dimension of graph algebras, European J. Combin. 27 (2006), no. 6, 962–970. MR 2226430, DOI 10.1016/j.ejc.2005.04.012
- László Lovász and Balázs Szegedy, Limits of dense graph sequences, J. Combin. Theory Ser. B 96 (2006), no. 6, 933–957. MR 2274085, DOI 10.1016/j.jctb.2006.05.002
- Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158
Bibliographic Information
- Balázs Szegedy
- Affiliation: Microsoft Research, One Microsoft Way, Redmond, Washington 98052
- Received by editor(s): May 2, 2005
- Published electronically: May 31, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 20 (2007), 969-988
- MSC (2000): Primary 05C99; Secondary 82B99
- DOI: https://doi.org/10.1090/S0894-0347-07-00568-1
- MathSciNet review: 2328712