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Autor:
Crass, Scott
In the late nineteenth century, Felix Klein revived the problem of solving the quintic equation from the moribund state into which Galois had placed it. Klein's approach was a mix of algebra and geometry built on the structure of the regular icosahed
Externí odkaz:
http://arxiv.org/abs/2006.01876
Autor:
Crass, Scott
Publikováno v:
Dynamical Systems: An International Journal 17, No. 2, June 2002
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.
Comment: 33 pages. arXiv admin note: text overlap with arXiv:math/9903054
Comment: 33 pages. arXiv admin note: text overlap with arXiv:math/9903054
Externí odkaz:
http://arxiv.org/abs/2003.01528
Akademický článek
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Autor:
Crass, Scott
Publikováno v:
Experimental Mathematics 23, No. 3, 2014, 261-270
Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedral equivariant map for which the icosahedron's twenty face-
Externí odkaz:
http://arxiv.org/abs/1404.3170
Autor:
Crass, Scott
In recent work on holomorphic maps that are symmetric under certain complex reflection groups---generated by complex reflections through a set of hyperplanes, the author announced a general conjecture related to reflection groups. The claim is that f
Externí odkaz:
http://arxiv.org/abs/1106.3304
Autor:
Crass, Scott
There is a family of seventh-degree polynomials $H$ whose members possess the symmetries of a simple group of order 168. This group has an elegant action on the complex projective plane. Developing some of the action's rich algebraic and geometric pr
Externí odkaz:
http://arxiv.org/abs/math/0601394
Autor:
Crass, Scott
The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For each such
Externí odkaz:
http://arxiv.org/abs/math/0307057
Autor:
Crass, Scott
Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map posseses "re
Externí odkaz:
http://arxiv.org/abs/math/9903111
Autor:
Crass, Scott, Doyle, Peter
Publikováno v:
International Mathematics Research Notices, 1997, No.2, 83-99
Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map posseses "re
Externí odkaz:
http://arxiv.org/abs/math/9903106