  In this article, we are interested in the enumeration of Fully Packed Loops
configurations on a grid with a given noncrossing matching. These quantities
also appear as the groundstate components of the Completely Packed Loops model
as conjectured by Razumov and Stroganov and recently proved by Cantini and
Sportiello. When considering matchings with p nested arches these quantities
are known to be polynomials. In a recent article, Fonseca and Nadeau
conjectured some unexpected properties of these polynomials, suggesting that
these quantities could be combinatorially interpreted even for negative p.
Here, we prove some of these conjectures. Notably, we prove that for negative p
we can factor the polynomials into two parts a "positive" one and a "negative"
one. Also, a sum rules of the negative part is proven.
