The Razumov–Stroganov conjecture relates the ground-state coefficients in the periodic even-length dense O(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.

Proof of the Razumov–Stroganov conjecture / L. Cantini, A. Sportiello. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - 118:5(2011), pp. 1549-1574. [10.1016/j.jcta.2011.01.007]

Proof of the Razumov–Stroganov conjecture

A. Sportiello
Ultimo
2011

Abstract

The Razumov–Stroganov conjecture relates the ground-state coefficients in the periodic even-length dense O(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.
fully-packed loop model ; alternating sign matrices ; dense loop model ; XXZ quantum spin chain
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
2011
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/156227
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