no. 6
Determinant formulae for some tiling problems and application to fully packed loops
[Formules de déterminants pour quel\-ques problèmes de pavage et application aux modèles de boucles compactes]
Di Francesco, Philippe1 ; Zinn-Justin, Paul ; Zuber, Jean-Bernard
1 CEA-Saclay, service de physique théorique de Saclay, CEA/DSM/SPhT, URA 2306 du CNRS, 91191 Gif sur Yvette Cedex (France), Independent University, LIFR-MIIP, 119002, Bolshoy Vlasyevskiy Pereulok 11, Moscow (Russie), Université Paris-Sud, laboratoire de physique théorique et modèles statistiques, UMR 8626 du CNRS, bâtiment 100, 91405 Orsay Cedex (France), Université Paris 6, LPTHE, Tour 24, 75231 Paris Cedex 05 (France)
Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2025-2050.

Quelques formules de déterminants sont données pour le dénombrement des pavages dans différents domaines, en relation avec les énumérations de matrices à signes alternés et de boucles compactes.

We present a number of determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.

DOI : 10.5802/aif.2150
Classification : 05A19, 52C20, 82B20
Keywords: Tilings, alternating sign matrices, fully packed loops
Mot clés : pavages, matrices à signes alternés, boucles compactes

Di Francesco, Philippe 1 ; Zinn-Justin, Paul  ; Zuber, Jean-Bernard 

1 CEA-Saclay, service de physique théorique de Saclay, CEA/DSM/SPhT, URA 2306 du CNRS, 91191 Gif sur Yvette Cedex (France), Independent University, LIFR-MIIP, 119002, Bolshoy Vlasyevskiy Pereulok 11, Moscow (Russie), Université Paris-Sud, laboratoire de physique théorique et modèles statistiques, UMR 8626 du CNRS, bâtiment 100, 91405 Orsay Cedex (France), Université Paris 6, LPTHE, Tour 24, 75231 Paris Cedex 05 (France) 
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     title = {Determinant formulae for some tiling problems and application to fully packed loops},
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Di Francesco, Philippe; Zinn-Justin, Paul; Zuber, Jean-Bernard. Determinant formulae for some tiling problems and application to fully packed loops. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2025-2050. doi : 10.5802/aif.2150. https://aif.centre-mersenne.org/articles/10.5802/aif.2150/

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