We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product whose factors are sums of squares of values of trigonometric functions. We provide a new derivation of the formula due to Kasteleyn and to Temperley and Fisher for counting the number of domino tilings of a $2m \times 2n$ rectangular checkerboard and a new way of counting the number of domino tilings of a $2m \times 2n$ checkerboard on a Möbius strip.
Laura Florescu
1
;
Daniela Morar
2
;
David Perkinson
3
;
Nicholas Salter
4
;
Tianyuan Xu
5
1
New York University
2
University of Michigan
3
Reed College
4
University of Chicago
5
University of Oregon
Laura Florescu; Daniela Morar; David Perkinson; Nicholas Salter; Tianyuan Xu. Sandpiles and dominos. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4472
@article{10_37236_4472,
author = {Laura Florescu and Daniela Morar and David Perkinson and Nicholas Salter and Tianyuan Xu},
title = {Sandpiles and dominos},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4472},
zbl = {1308.05059},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4472/}
}
TY - JOUR
AU - Laura Florescu
AU - Daniela Morar
AU - David Perkinson
AU - Nicholas Salter
AU - Tianyuan Xu
TI - Sandpiles and dominos
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4472/
DO - 10.37236/4472
ID - 10_37236_4472
ER -
%0 Journal Article
%A Laura Florescu
%A Daniela Morar
%A David Perkinson
%A Nicholas Salter
%A Tianyuan Xu
%T Sandpiles and dominos
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4472/
%R 10.37236/4472
%F 10_37236_4472
