Compression of transfer matrices
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
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.
transfer matrix, enumeration, independent sets, matchings, 3D dimer constant, polygraph
IdentifiersURN: urn:nbn:se:kth:diva-20498ISI: 000167835300030OAI: oai:DiVA.org:kth-20498DiVA: diva2:339193
QC 201005252010-08-102010-08-102011-11-17Bibliographically approved