Klein quartic chromatic number
Webit lets one show that a certain model of the Klein quartic curve mod 2 is the unique curve of genus 3 with the maximal number of points over the field of 213elements (see my article on the Klein quartic in “The Eightfold Way”); and in coding theory, it seems to promise a perfect 2-error-correcting binary code http://sections.maa.org/mddcva/MeetingFiles/Fall2014Meeting/TalkSlides/Perng.pdf
Klein quartic chromatic number
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WebKlein quartic Khas been conjectured to maximize 1 in [Coo18, Conjecture 5.2]. Numerical calculations from [Coo18, Table D.1] suggest that 1(K) ˇ2:6767 and m 1(K) = 8 = 2g+ 2: In … http://math.bu.edu/people/ep/Accola/Farrington.pdf
Webthe chromatic number of any 6-regular Klein bottle graph is at least 3 and at most 6. The following is an immediate consequence of Theorem 5, since a unique 6-chromatic 6-regular graph Kh(2,3) is non-simple and contains K6 as a subgraph. Corollary 6 Every 6-regular simple graph on the Klein bottle is 5-colorable. More- The Klein quartic can be viewed as a projective algebraic curve over the complex numbers C, defined by the following quartic equation in homogeneous coordinates [x:y:z] on P (C): $${\displaystyle x^{3}y+y^{3}z+z^{3}x=0.}$$ The locus of this equation in P (C) is the original Riemannian surface that Klein … See more In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation … See more It is important to distinguish two different forms of the quartic. The closed quartic is what is generally meant in geometry; topologically it has … See more The Klein quartic admits tilings connected with the symmetry group (a "regular map" ), and these are used in understanding the symmetry group, … See more Little has been proved about the spectral theory of the Klein quartic. Because the Klein quartic has the largest symmetry group of surfaces in its topological class, much like the See more The compact Klein quartic can be constructed as the quotient of the hyperbolic plane by the action of a suitable Fuchsian group Γ(I) … See more The Klein quartic can be obtained as the quotient of the hyperbolic plane by the action of a Fuchsian group. The fundamental domain is a regular 14-gon, which has area $${\displaystyle 8\pi }$$ by the Gauss-Bonnet theorem. This can be seen in the adjoining … See more The Klein quartic cannot be realized as a 3-dimensional figure, in the sense that no 3-dimensional figure has (rotational) symmetries equal to … See more
WebUnlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, … WebKlein’s quartic curve is a surface of genus 3 (a three-holed torus) of constant negative curvature. It can be constructed by specifying a 14-gon in the hyperbolic plane and …
WebFeb 5, 2024 · For the standard order-3 heptagonal tiling of the Klein quartic K, we have m = 3 and n = 7, so χ ( K) = ( 2 / 3 − 1 + 2 / 7) E = − 1 21 E = − 1 6 F. Since χ ( K) = − 4, we find F = 24.
WebWe describe the Klein quartic X and highlight some of its remarkable properties that are of particular interest in number theory. These include extremal properties in … asppen paladioWebThe name \Klein quartic" or \Klein curve" refers to an algebraic description of the ideal surface that the sculpture represents, determined by the equation x3y+y3+x= 0. (This equation is called a quartic or 4th-degree equation because the highest termx3yhas 3x’s and 1y, making degree 4 in all.) asppa tehuacanWebSee here a general method to create a Klein bottle. The Möbius strip is a one-sided surface (with one face), therefore is not orientable, of genus 2, zero Euler characteristic , and … aspp perusahaan apaWebOutline Introduction Automorphism Group Aut(X) of the Klein Quartic XAut(X) is a simple group of order 168The Klein Quartic Theorem. (Klein, 1879) Assume char k ̸= 3. If X is the curve given by x3y +y3z +z3x = 0; the group Aut X is the simple group of order 168, whose order is the maximum 84(g −1) allowed by curves of genus 3.Note. asppi perugiaWebLOCATION. 320 SW Grover St, Portland, Oregon 97239 [email protected] Phone: (503) 746-5354. Monday – Friday 9:00am – 6:00pm Closed Saturday/Sunday asppi bariWebThe Klein Quartic in Number Theory NOAM D. ELKIES Abstract. We describe the Klein quartic X and highlight some of its re-markable propertiesthat are of particularinterest in … asppi bergamo orariWebThis graph is a 3-regular graph with 56 vertices and 84 edges, named after Felix Klein.It is a Hamiltonian graph. It has chromatic number 3, chromatic index 3, radius 6, diameter 6 and girth 7. It is also a 3-vertex-connected and a 3-edge-connected graph.It has book thickness 3 and queue number 2.. It can be embedded in the genus-3 orientable surface (which can be … aspr barda