Twodimensional monomerdimer systems are computationally intractable
 Mark Jerrum
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The classic problem of counting monomerdimer arrangements on a twodimensional lattice is analyzed using techniques from theoretical computer science. Under a certain assumption, made precise in the text, it can be shown that the general problem is computationally intractable. This negative result contrasts with the special case of a system with monomer density zero, for which efficient solutions have been known for some time. A second, much easier result, obtained under the same assumption, is that the partition function of a threedimensional Ising system is computationally intractable. Again, the negative result contrasts with known efficient techniques for evaluating the partition function of a twodimensional system.
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 Title
 Twodimensional monomerdimer systems are computationally intractable
 Journal

Journal of Statistical Physics
Volume 48, Issue 12 , pp 121134
 Cover Date
 19870701
 DOI
 10.1007/BF01010403
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Computational complexity
 Ising model
 monomerdimer system
 #Pcompleteness
 Industry Sectors
 Authors

 Mark Jerrum ^{(1)}
 Author Affiliations

 1. Department of Computer Science, University of Edinburgh, EH9 3JZ, Edinburgh, Scotland