Hypercubic billiard word: Difference between revisions
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== Properties == | == Properties == | ||
Proofs to be added | Proofs to be added | ||
* A scale word is a rank-2 billiard scale iff it is a MOS scale. | * A circular scale word is a rank-2 billiard scale iff it is a MOS scale. | ||
* Not all billiard scales are Fokker blocks; [[blackdye]] can be checked to be a billiard scale by using the initial position (1, 1/√5, 1/√3), but it is not a Fokker block. | * Not all billiard scales are Fokker blocks; [[blackdye]] can be checked to be a billiard scale by using the initial position (1, 1/√5, 1/√3), but it is not a Fokker block. | ||
* A billiard scale becomes a billiard scale of lower rank when one removes all instances of some subset of its step sizes. However, the converse is false. | * A billiard scale becomes a billiard scale of lower rank when one removes all instances of some subset of its step sizes. However, the converse is false. | ||