The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Bayati, Mohsen; Gamarnik, David; Katz, Dimitriy; Nair, Chandra; Tetali, Prasad. Simple deterministic approximation algorithms for counting matchings. STOC'07—Proceedings of the 39th Annual ACM Symposium on Theory of Computing, 122--127, ACM, New York, 2007. MR2402435
  • Caianiello, E. R. Combinatorics and renormalization in quantum field theory. Frontiers in Physics. W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1973. xv+121 pp. MR0464973
  • M.E. Fisher. On the dimer solution of planar Ising models, J. of Math. Phys. 7 (1966), 1776--1781.
  • Fishman, George S., Monte Carlo. Concepts, algorithms, and applications. Springer Series in Operations Research. Springer-Verlag, New York, 1996. xxvi+698 pp. ISBN: 0-387-94527-X MR1392474
  • Huber, Mark. Simulation reductions for the Ising model, J. Stat. Theory Pract., to appear.
  • Jerrum, Mark and Sinclair, Alistair. Approximating the permanent. SIAM J. Comput. 18 (1989), no. 6, 1149--1178. MR1025467
  • Jerrum, Mark and Sinclair, Alistair. Polynomial-time approximation algorithms for the Ising model. SIAM J. Comput. 22 (1993), no. 5, 1087--1116. MR1237164
  • M. Jerrum and A. Sinclair. The Markov chain Monte Carlo method: An approach to approximate counting and integration, pp. 482--520, PWS, 1996.
  • Jerrum, Mark R.; Valiant, Leslie G.; Vazirani, Vijay V. Random generation of combinatorial structures from a uniform distribution. Theoret. Comput. Sci. 43 (1986), no. 2-3, 169--188. MR0855970
  • R. Karp, Approximate counting and sampling [lecture notes], Recorded by Alexandre Bouchard-Côté, http://www.cs.berkeley.edu/~karp/greatalgo/lecture16.pdf.
  • Law, Wai Jing. Approximately counting perfect and general matchings in bipartite and general graphs. Thesis (Ph.D.)–Duke University. ProQuest LLC, Ann Arbor, MI, 2009. 227 pp. ISBN: 978-1109-08252-4 MR2712989
  • Montroll, Elliott W. Lattice statistics, Applied combinatorial mathematics. University of California Engineering and Physical Sciences Extension Series John Wiley and Sons, Inc., New York-London-Sydney, 1964, MR0174486
  • Newell, Gordon F.; Montroll, Elliott W. On the theory of the Ising model of ferromagnetism. Rev. Modern Physics 25, (1953). 353--389. MR0056511
  • Papadimitriou, Christos H.; Steiglitz, Kenneth. Combinatorial optimization: algorithms and complexity. Dover Publications, Inc., Mineola, NY, 1998. xvi+496 pp. ISBN: 0-486-40258-4 MR1637890
  • Sinclair, Alistair. Algorithms for random generation and counting. A Markov chain approach. Progress in Theoretical Computer Science. Birkhäuser Boston, Inc., Boston, MA, 1993. vi+146 pp. ISBN: 0-8176-3658-7 MR1201590
  • B. L. van~der Waerden, Die lange Reichweite der regelmässigen Atomanordnung in Mischkristallen, Z. Physik 118 (1941), 473--488.
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.