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Types of Flocks

In the next few sections we will examine several general classes of flocks of cones. We have already studied Linear flocks and Star Flocks, and have seen the definitions of Fisher type flocks and FTW type flocks. The flocks that we wish to consider here are those that have a geometric description. Except for the linear and star flocks, the flocks on this list were all discovered first for quadratic cones and with the additional exception of the Fisher type flocks all were initially described algebraically. What we are doing is to take these flocks and when a geometric property possessed by the flock is known to exist, use that geometric property as the definition of a flock type. The naming convention is to use the name of the flock in the quadratic cone setting and append the word "type" to it. Thus, one of the classes of flocks of quadratic cones are the semi-field flocks. These flocks are most easily described algebraically by defining them to be those flocks for which the coordinate functions of the normalized representation are all additive functions. We will however provide a geometric description of this class of flocks and use it as the definition for a type of flock over an arbitrary cone, and call them semi-field type flocks.

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