![]() ![]() To finish the process, select Search for another application on this PC and, using the file browser, select the installation folder for your ZIP software. Launch WinZIP from the Start menu or Desktop.Download WinZIP application from and launch it by double-clicking on it.Confirm by checking "Always use this application" to open ZI files and clicking on the OK button. Select files and folders you want to extract and click on the "Extract to" icon.You will see contents of the ZI file and every file and folder stored in it.In the file open dialog select ZI file you want to open and click "Open".Click on File->Open archive in the WinZIP main menu. Get more information about how to open ZI file. ![]() In this post I wish to discuss flock generalised quadrangles.If you are not able to open file with certain file extension make sure to check if extension for the file is correct. As mentioned in the first of this series, John has already discussed these a bit in a previous post so my main aim will be to flesh that out and provide more background. I have relied heavily on Maska Law’s PhD thesis which is available from Ghent’s PhD theses in finite geometry page. Recall that a conic is the set of zeros of a nondegenerate quadratic form on. Embed as a hyperplane in and take a point not on. For each of the points of there is a unique line through such a point and. Let be the set of all points on these lines. The set is called a quadratic cone with vertex. Now acts transitively on the set of pairs of points and hyperplanes of where does not contain, and the stabiliser of such a pair induces on and so acts transitively on the set of conics contained in. Thus all quadratic cones of are equivalent.Īn easy way to construct a quadratic cone is to take the zeros of the degenerate quadratic form, where. Note that for any plane of the set of zeros of on forms a conic. This is all reminiscent of the classical case of a cone in, where the intersections of a plane with the cone are the conic sections and are either a point, a circle, an ellipse, a parabola or a hyperbola.Ī flock of a quadratic cone with vertex is a partition of into disjoint conics. Each conic is the intersection of with a plane. Let be a line of which intersects trivially. Then is contained in planes, one of which contains. Each of the remaining planes containing meets each of the lines which make up and hence meets in points. Morever, since the intersection of two planes through is, the conics we obtain are all disjoint and so we get a flock. Such a flock is called a linear flock.Ī BLT-set of lines of is a set of disjoint lines such that no line of meets more than two lines of. BLT-sets are named after Laura Bader, Guglielmo Lunardon and Jef Thas who first studied them in 1990. Now let be a line of which meets some line of. Let be the point of intersection and suppose that does not meet any of the remaining lines of. Then for each line of, the GQ property implies that for each point on, is collinear with a unique point of and in particular there is a unique point of collinear with. Considering each of the lines of we obtain points collinear with. Since no line of meets more than 2 lines of, it follows that this gives lines incident with. Thus we have obtained lines incident with, contradicting the fact that each point of lies on exactly lines. Hence meets two lines of, that is, every line of meets 0 or 2 lines of. Īn example of a BLT-set is the linear one and is constructed as follows. ![]()
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