Mathematics – Combinatorics
Scientific paper
2011-06-20
Mathematics
Combinatorics
25 pages
Scientific paper
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.
No associations
LandOfFree
On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-177464