The crossing number of a knot is the minimum number of crossings in any two-dimensional diagram representing that knot.

The crossing number is a knot invariant. The crossing number of a knot is if and only if it is the unknot. The crossing number of the trefoil is 3.

The span of the Jones Polynomial of an alternating knot is equal to its crossing number. For nonalternating knots, this span is less than or equal to the crossing number.

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