  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.
