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Compression of transfer matrices
Umeå University, Department of Mathematics.
2001 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 231, no 03-jan, 321-329 p.Article in journal (Refereed) Published
Abstract [en]

We present a method for reducing the size of transfer matrices by exploiting symmetry. For example, the transfer matrix for enumeration of matchings in the graph C-4 x C-4 x P-n can be reduced from order 65536 to 402 simply due to the 384 automorphisms of C-4 x C-4. The matrix for enumeration of perfect matchings can be still further reduced to order 93, all in a straightforward and mechanical way. As an application we report an improved upper bound for the three-dimensional dimer problem.

Place, publisher, year, edition, pages
2001. Vol. 231, no 03-jan, 321-329 p.
Keyword [en]
transfer matrix, enumeration, independent sets, matchings, 3D dimer constant, polygraph
Identifiers
URN: urn:nbn:se:kth:diva-20498ISI: 000167835300030OAI: oai:DiVA.org:kth-20498DiVA: diva2:339193
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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