Combinatorial nature of ground state vector of O(1) loop model

Details Combinatorial nature of ground state vector of O(1) loop model Combinatorial nature of ground state vector of O(1) loop model

2001-04-24

arxiv.org/abs/math/0104216v2

Theor.Math.Phys. 138 (2004) 333-337; Teor.Mat.Fiz. 138 (2004) 395-400

Mathematics

Combinatorics

5 pages, LaTeX2e, DFPL is changed to FPL in accordance with a suggestion of J. Propp

Scientific paper

Hanging about a hypothetical connections between the ground state vector for some special spin systems and the alternating-sign matrices, we have found a numerical evidence for the fact that the numbers of the states of the fully packed loop model with fixed link-patterns coincide with the components of the ground state vector of the dense O$(1)$ loop model considered by Batchelor, de Gier and Nienhuis. Our conjecture generalizes in a sense the conjecture of Bosley and Fidkowski, refined by Cohn and Propp, and proved by Wieland.

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