Geodesic
Alternating-sign matrices and domino tilings. I
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 2, pp. 111-132.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order $n$ has exactly $2 ^{ n( n+1)/2}$ domino tilings. In this, the first half of a two-part paper, we give two proofs of this formula. The first proof exploits a connection between domino tilings and the alternating-sign matrices of Mills, Robbins, and Rumsey. In particular, a domino tiling of an Aztec diamond corresponds to a compatible pair of alternating-sign matrices. The second proof of our formula uses monotone triangles, which constitute another form taken by alternating-sign matrices; by assigning each monotone triangle a suitable weight, we can count domino tilings of an Aztec diamond.
Keywords: tiling, domino, alternating-sign matrix, monotone triangle, representation, square ice 
@article{JAC_1992__1_2_a4,
     author = {Elkies, Noam and Kuperberg, Greg and Larsen, Michael and Propp, James},
     title = {Alternating-sign matrices and domino tilings. {I}},
     journal = {Journal of Algebraic Combinatorics},
     pages = {111--132},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1992__1_2_a4/}
}
TY  - JOUR
AU  - Elkies, Noam
AU  - Kuperberg, Greg
AU  - Larsen, Michael
AU  - Propp, James
TI  - Alternating-sign matrices and domino tilings. I
JO  - Journal of Algebraic Combinatorics
PY  - 1992
SP  - 111
EP  - 132
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_1992__1_2_a4/
LA  - en
ID  - JAC_1992__1_2_a4
ER  - 
%0 Journal Article
%A Elkies, Noam
%A Kuperberg, Greg
%A Larsen, Michael
%A Propp, James
%T Alternating-sign matrices and domino tilings. I
%J Journal of Algebraic Combinatorics
%D 1992
%P 111-132
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_1992__1_2_a4/
%G en
%F JAC_1992__1_2_a4
Elkies, Noam; Kuperberg, Greg; Larsen, Michael; Propp, James. Alternating-sign matrices and domino tilings. I. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 2, pp. 111-132. http://geodesic.mathdoc.fr/item/JAC_1992__1_2_a4/