Theory of computation of multidimensional entropy with an application to the monomer–dimer problem

• Published in: Advances in applied mathematics Vol. 34; no. 3; pp. 486 - 522
• Main Authors: Friedland, Shmuel, Peled, Uri N.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2005
• Subjects: Monomer-dimer; Subshifts of finite type; Topological entropy; Transfer matrix; Transfer matrix; Subshifts of finite type; Topological entropy; Monomer-dimer

Consider all colorings of a finite box in a multidimensional grid with a given number of colors subject to given local constraints. We outline the most recent theory for the computation of the exponential growth rate of the number of such colorings as a function of the dimensions of the box. As an a...