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Séminaire Lotharingien de Combinatoire, B56e (2007), 29 pp.

# Johan Thapper

# Refined Counting of Fully Packed Loop Configurations

**Abstract.**
We give a generalisation of a conjecture by Propp on a summation
formula for fully packed loop configurations.
The original conjecture states that the number of
configurations in which each external edge is connected to its
neighbour is equal to the total number of configurations of size one
less.
This conjecture was later generalised by Zuber to include more types
of configurations.
Our conjecture further refines the counting and provides a general
framework for some other summation formulas observed by Zuber.
It also implies similar summation formulas for half-turn symmetric
configurations.

Received: October 2, 2006.
Accepted: April 6, 2007.
Final Version: June 4, 2007.

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