$O(1)$ 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
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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.
@article{TMF_2005_142_2_a6,
author = {A. V. Razumov and Yu. G. Stroganov},
title = {$O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {284--292},
publisher = {mathdoc},
volume = {142},
number = {2},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a6/}
}
TY - JOUR AU - A. V. Razumov AU - Yu. G. Stroganov TI - $O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2005 SP - 284 EP - 292 VL - 142 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a6/ LA - ru ID - TMF_2005_142_2_a6 ER -
%0 Journal Article %A A. V. Razumov %A Yu. G. Stroganov %T $O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices %J Teoretičeskaâ i matematičeskaâ fizika %D 2005 %P 284-292 %V 142 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a6/ %G ru %F TMF_2005_142_2_a6
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/