On FPL configurations with four sets of nested arches
نویسنده
چکیده
The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a, b, c, d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindström-GesselViennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a, b, c, d) = 1 or 2. AMS Subject Classification (2000): Primary 05A19; Secondary 52C20, 82B20
منابع مشابه
A Bijection Between Classes of Fully Packed Loops and Plane Partitions
It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a × b × c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions.
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