We study partition functions for the dimer model on families of finite graphs converging to infinite self-similar graphs and forming approximation sequences to certain well-known fractals. The graphs that we consider are provided by actions of finitely generated groups by automorphisms on rooted trees, and thus their edges are naturally labeled by the generators of the group. It is thus natural to consider weight functions on these graphs taking different values according to the labeling. We study in detail the well-known example of the Hanoi Towers group H-(3), closely related to the Sierpinski gasket. (c) 2012 Elsevier Ltd. All rights reserved.
Counting dimer coverings on self-similar Schreier graphs / Daniele, Dangeli; Donno, Alfredo; Tatiana, Nagnibeda. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - 33:7(2012), pp. 1484-1513. [10.1016/j.ejc.2012.03.014]
Counting dimer coverings on self-similar Schreier graphs
DONNO, Alfredo;
2012
Abstract
We study partition functions for the dimer model on families of finite graphs converging to infinite self-similar graphs and forming approximation sequences to certain well-known fractals. The graphs that we consider are provided by actions of finitely generated groups by automorphisms on rooted trees, and thus their edges are naturally labeled by the generators of the group. It is thus natural to consider weight functions on these graphs taking different values according to the labeling. We study in detail the well-known example of the Hanoi Towers group H-(3), closely related to the Sierpinski gasket. (c) 2012 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
