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Polyknight

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Polyknight

A polyknight is a plane geometric figure formed by selecting cells in a square lattice that could represent the path of a chess knight in which doubling back is allowed. It is a polyform with square cells which are not necessarily connected, comparable to the polyking. Alternatively, it can be interpreted as a connected subset of the vertices of a knight's graph, a graph formed by connecting pairs of lattice squares that are a knight's move apart.

Free, one-sided, and fixed polyknights

Three common ways of distinguishing polyominoes for enumeration can also be extended to polyknights:

  • free polyknights are distinct when none is a rigid transformation (translation, rotation, reflection or glide reflection) of another (pieces that can be picked up and flipped over).
  • one-sided polyknights are distinct when none is a translation or rotation of another (pieces that cannot be flipped over).
  • fixed polyknights are distinct when none is a translation of another (pieces that can be neither flipped nor rotated).
  • The following table shows the numbers of polyknights of various types with n cells.

    References

    Polyknight Wikipedia


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