期刊
JOURNAL OF COMBINATORIAL THEORY SERIES A
卷 118, 期 5, 页码 1549-1574出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcta.2011.01.007
关键词
Fully-packed loop model; Alternating sign matrices; Dense loop model; XXZ quantum spin chain
类别
资金
- ANR [ANR-06-BLAN-0058-01]
- Agence Nationale de la Recherche (ANR) [ANR-06-BLAN-0058] Funding Source: Agence Nationale de la Recherche (ANR)
The Razumov-Stroganov conjecture relates the ground-state coefficients in the periodic even-length dense 0(1) loop model to the enumeration of fully-packed loop configurations on the square, with alternating boundary conditions, refined according to the link pattern for the boundary points. Here we prove this conjecture, by means of purely combinatorial methods. The main ingredient is a generalization of the Wieland proof technique for the dihedral symmetry of these classes, based on the 'gyration' operation, whose full strength we will investigate in a companion paper. (C) 2011 Elsevier Inc. All rights reserved.
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