Thursday, May 18, 2006

Thursday May 18

Every overlapping combination of rhombus inequalities with no dependence on the interior is a positive combination of nonoverlapping ones, and every nonoverlapping combination can be uniquely labeled to make a puzzle. (We didn't, and won't, prove these.)
Harder fact: the only puzzles that give important inequalities are the ones that can filled in uniquely given their boundary.
Deflation of puzzles. Consequences for the number of each kind of piece.
The puzzle ring for (n,k), and its relation to the hive ring. (We have yet to prove that the natural map is a ring homomorphism.)
Definition of honeycombs.

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