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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94973Hanging 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.5 pages, LaTeX2e, DFPL is changed to FPL in accordance with a suggestion of J. ProppCombinatoricsCondensed MatterHigh Energy Physics - TheoryMathematical PhysicsCombinatorial nature of ground state vector of O(1) loop modeltext