Results 221 to 230 of about 29,075 (258)

The Translation Planes of Dempwolff

Canadian Journal of Mathematics, 1981
In [2], Dempwolff constructs three translation planes of order 16 using sharply 2-transitive sets of permutations in S16. That is, if acting on Λ is a sharply 2-transitive set of permutations then an affine plane of order n may be defined as follows: The set of points = {(x, y)|x, y ∊ Λ} and the lines = {(x, y)|y = xg for fixed }, {(x, y)|x = c}, {(x,
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Translating polygons in the plane

2005
Let P = (p1,...,pn) and Q = (q1,...,qm) be two simple polygons with non-intersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to
Jörg-Rüdiger Sack, Godfried T. Toussaint   +1 more
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SOME CLASSES OF TRANSLATION PLANES

The Quarterly Journal of Mathematics, 1984
This article considers the following. Let \(\pi\) be a finite translation plane of order \(p^ r\) with an autotopism group G which has an orbit of length \(p^ r\)-p on \(\ell_{\infty}\), the line at infinity. The authors make the following additional assumptions: (a) p is an odd prime and \(r=2\); (b) G acts faithfully on \(\ell_{\infty}\).
Cohen, Stephen D., Ganley, Michael J.
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Ovoids and Translation Planes

Canadian Journal of Mathematics, 1982
An ovoid in an orthogonal vector space V of type Ω+(2n, q) or Ω(2n – 1, q) is a set Ω of qn–1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [12], [6]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q2, via the Klein correspondence ...
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Ovoidal translation planes

Archiv Der Mathematik, 1972
exaly   +2 more sources

Doubly β-Derived Translation Planes

Designs, Codes and Cryptography, 2003
Let \(q>3\) be an odd prime power. A chain of circles in the Miquelian inversive plane \(M(q)\) is a collection of \({1\over 2}(q+3)\) circles such that every point covered by some circle in this set lies on exactly two circles from the collection. Using the correspondence between points and circles of \(M(q)\) and lines and reguli of a regular spread \
Abatangelo, V., Larato, Bambina
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Pencils of translation ovals in translation planes

Geometriae Dedicata, 1994
Let \({\mathcal T}\) be a translation plane of even order \(q\) with translation line \(I_ \infty\). An oval \({\mathcal O}\) in \({\mathcal T}\) is called a translation oval if \(I_ \infty\) is a tangent at a point \(a\) and if the stabilizer of \({\mathcal O}\) in the translation group acts transitively on \({\mathcal O}\setminus\{a\}\).
Glynn, D. G., Steinke, G. F.
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On Translations in General Plane Geometries

American Journal of Mathematics, 1938
In a well-known paper, Hilbelt 1 has characterized the Euclidean and hyperbolic plane geometries by mere group and continuity axioms. He gets all the motions at once by requiring the existence of sufficiently many rotations. The present paper tries to point out how the existence of more and more translations gradually specializes the rather general ...
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A Classification of Semi-Translation Planes

Canadian Journal of Mathematics, 1969
The classification of certain types of projective planes has recently been of considerable interest to both geometers and group theorists. Due in part to the current general interest in finite mathematics and the developments connecting group theory and finite geometry, the Lenz-Barlotti classification of finite projective planes (2; 10), in particular,
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Quasigroups and translation planes

Journal of Geometry, 1992
A quasigroup \((Q,\cdot)\) is said to be medial if \((x\cdot y)\cdot(z\cdot t)=(x\cdot z)\cdot(y\cdot t)\) for all \(x,y,z,t\in Q\), and is called idempotent if \(x\cdot x=x\) for all \(x\in Q\). If \((R,+,\cdot)\) is the coordinatizating ring of a translation plane and the kernel of \(R\) contains at least one element \(k\) distinct from 0 and 1, then
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