Fully Packed Loops in a triangle: matchings, paths and puzzles
Presented by Mrs. Ilse FISCHER
Type: Oral presentation
Fully Packed Loop configurations (FPLs) are subgraphs of a square grid such that each internal node is of degree two. While these objects arise naturally in a statistical physics context as a model for ice, they also lead to intriguing enumerative problems. Fully Packed Loop configurations in a triangle (TFPLs) first appeared in the study of ordinary Fully Packed Loop configurations where they were used to show that the number of FPLs with a given link pattern that has m nested arches is a polynomial function in m. It soon turned out that TFPLs possess a number of other nice properties. For instance, they can be seen as a generalized model for Littlewood-Richardson coefficients, thereby establishing an unexpected link to algebra. I will present a new combinatorial approach to the enumeration of TFPLs.