Geodesic
$O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 284-292 Cet article a éte moissonné depuis la source Math-Net.Ru

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This work is a continuation of our recent paper where we discussed numerical evidence that the numbers of the states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the $O(1)$ loop model with periodic boundary conditions and an even number of sites. We give two new conjectures related to different boundary conditions: we suggest and numerically verify that the numbers of the half-turn symmetric states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the $O(1)$ loop model with periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of open boundary conditions and an even number of sites.
Keywords: loop model, ground state, fully packed loop model, alternating-sign matrices. 
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     title = {$O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices},
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A. V. Razumov; Yu. G. Stroganov. $O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 284-292. http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a6/

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