Gauss notation (also known as a Gauss code or Gauss words) is a

notation In linguistics and semiotics, a notation system is a system of graphics or symbols, Character_(symbol), characters and abbreviated Expression (language), expressions, used (for example) in Artistic disciplines, artistic and scientific disciplines ...

for mathematical knots. It is created by enumerating and classifying the crossings of an embedding of the knot in a plane. It is named after the German mathematician

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...

(1777–1855). Gauss code represents a knot with a sequence of integers. However, rather than every crossing being represented by two different numbers, crossings are labelled with only one number. When the crossing is an overcrossing, a positive number is listed. At an undercrossing, a negative number. For example, the trefoil knot in Gauss code can be given as: 1,−2,3,−1,2,−3. Gauss code is limited in its ability to identify knots by a few problems. The starting point on the knot at which to begin tracing the crossings is arbitrary, and there is no way to determine which direction to trace in. Also, the Gauss code is unable to indicate the handedness of each crossing, which is necessary to identify a knot versus its mirror. For example, the Gauss code for the trefoil knot does not specify if it is the right-handed or left-handed trefoil. See p. 274 This last issue is often solved by using the extended Gauss code. In this modification, the positive/negative sign on the second instance of every number is chosen to represent the handedness of that crossing, rather than the over/under sign of the crossing, which is made clear in the first instance of the number. A right-handed crossing is given a positive number, and a left handed crossing is given a negative number.

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