Representation & Behaviour - Rational Tangle Dance

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Four people stand at positions A, B, C and D and hold two ropes in the initial configuration shown.

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These folk may “dance” with these ropes by performing just two moves, multiple times, in any order they like:

  • Rotate as a group 90 degree counterclockwise. (Thus the person in position A moves to position B, the person in position B to position C, and so on.) Call this move “ROTATE”denoted as R.

    Example: Given initial state, on one rotate, below is the state:

    enter image description here

  • Folks in positions D and C(the folks in the northeast and southeast) swap places with D holding the rope up and over C. Call this move a “SWAP.” denoted as T.

    Example: Given initial state, on one swap, below is the state:

    enter image description here


ROTATE - R

SWAP - T

Properties of operations:

  • Operations are not commutative - RRRTT not equals RTRTR

  • Operations are associative - (TR)T equals T(RT)

  • Inverse - R^-1 = R^3 or 3R and T^-1 = RTRTR

    R^-1 (one anti-clockwise rotation) is:

    enter image description here

    3R (three clockwise rotation) is:

    enter image description here


  1. How to represent the state of this tangle with an abstract data type?

  2. How do the operations(ROTATE & SWAP) modify the state of this tangle represented by this abstract data type?

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