Computing The Linking Number
There is an algorithm to compute the linking number of two curves from a link diagram. Label each crossing as positive or negative, according to the following rule:
The total number of positive crossings minus the total number of negative crossings is equal to twice the linking number. That is:
where n1, n2, n3, n4 represent the number of crossings of each of the four types. The two sums and are always equal, which leads to the following alternative formula
Note that involves only the undercrossings of the blue curve by the red, while involves only the overcrossings.
Read more about this topic: Linking Number
Famous quotes containing the word number:
“Mining today is an affair of mathematics, of finance, of the latest in engineering skill. Cautious men behind polished desks in San Francisco figure out in advance the amount of metal to a cubic yard, the number of yards washed a day, the cost of each operation. They have no need of grubstakes.”
—Merle Colby, U.S. public relief program (1935-1943)