Karger's algorithm - Revision history

en>Ecnerwala: /* Analysis */ Fixed math.

2014-05-28T21:39:17Z

Analysis: Fixed math.

← Older revision		Revision as of 23:39, 28 May 2014
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en>Zackchase at 19:41, 10 February 2014

2014-02-10T19:41:50Z

← Older revision		Revision as of 21:41, 10 February 2014
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	A '''convex lattice polytope''' (also called '''Z-polyhedron''' or '''Z-polytope''') is a [[geometry\|geometric]] object playing an important role in [[discrete geometry]] and [[combinatorial commutative algebra]]. It is ~~a [[polytope]] in a Euclidean space '''R'''<sup>n</sup> which~~ is ~~a [[convex hull]] of finitely many points in~~ the [~~[integer lattice]] '''Z'''<sup>n<~~/~~sup> ⊂ '''R'''<sup>n<~~/~~sup>~~. ~~Such objects are prominently featured in the theory of [[toric variety\|toric varieties]], where they correspond to polarized projective toric varieties~~.		Hi there. My name is Sophia Meagher even though it is not the name on my beginning certification. Credit authorising [http://formalarmour.com/index.php?do=/profile-26947/info/ cheap psychic readings] is how she tends to make a living. What me and my family love is bungee leaping but I've been taking on new issues recently. Some time in the past she selected to reside in Alaska and her mothers and fathers live nearby.<br><br>my site :: [http://www.article-galaxy.com/profile.php?a=143251 phone psychic] readings ([http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ alles-herunterladen.de])

	=~~= Examples ==~~
	* An ''n''-~~dimensional [[simplex~~]~~] Δ in '''R'''<sup>n+1</sup>~~ is ~~the convex hull of ''n''+1 points that do not lie on~~ a ~~single affine hyperplane~~. ~~The simplex is a convex lattice polytope if (~~and ~~only if) the vertices have integral coordinates. The corresponding toric variety~~ is ~~the~~ '~~'n''-dimensional [[projective space]] '''P'''<sup>n</sup>~~.
	* The [[unit cube]] in ~~'''R'''<sup>n</sup>, whose vertices are~~ the ~~''2''~~<~~sup~~>n<~~/sup~~> ~~points all of whose coordinates are ''0'' or ''1'', is a convex lattice polytope. The corresponding toric variety is the~~ [~~[Segre embedding]] of the ''n''-fold product of the projective line '''P'''<sup>1<~~/~~sup>~~.
	* In the special case of two-~~dimensional convex lattice polytopes in '''R'''<sup>2</sup>, they are also known as '''convex lattice polygons'''~~.
	* In [[algebraic geometry]], an important instance of lattice polytopes called the '''Newton polytopes''' are the convex hulls of the set <math>A</~~math> which consists of all the exponent vectors appearing in a collection of monomials~~. ~~For example, consider the polynomial of the form <math>axy+bx^2+cy^5+d</math> with <math>a,b,c,d \neq 0</math> has~~ a ~~lattice equal to the triangle~~
	~~:<math>{\rm conv}(\{(1,1),(2,0),(0,5),(0,0)\}).\ </math>~~

	~~== See also =~~=

	* [[Normal polytope]]
	* [~~[Pick's theorem]]~~
	* [[Ehrhart polynomial]]
	* [[Integer points in convex polyhedra]]

	~~== References ==~~
	* Ezra Miller, [[Bernd Sturmfels]], ''Combinatorial commutative algebra''. ~~Graduate Texts in Mathematics, 227. Springer~~-~~Verlag, New York, 2005. xiv+417 pp. ISBN 0~~-~~387~~-~~22356~~-8

	~~{{geometry~~-~~stub}}~~
	~~[[Category:Polytopes]]~~
	~~[[Category:Lattice points]~~]

en>Qwertyus: /* Success probability of the contraction algorithm */ copula

2014-01-30T23:05:31Z

Success probability of the contraction algorithm: copula

← Older revision		Revision as of 01:05, 31 January 2014
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	~~Wilber Berryhill~~ is ~~the title his mothers~~ and ~~fathers gave him and he totally digs that title~~. ~~Ohio~~ is ~~exactly~~ where ~~his home~~ is ~~and his family members enjoys it~~. ~~Credit authorising~~ is ~~how he tends to make money~~. ~~To climb~~ is ~~some thing she would by no means give up~~.<br><br>~~my weblog; love psychic (~~[~~http:~~//~~fashionlinked~~.~~com~~/~~index~~.~~php?do=~~/~~profile-13453~~/~~info~~/ ~~redirected here~~])		A '''convex lattice polytope''' (also called '''Z-polyhedron''' or '''Z-polytope''') is a [[geometry\|geometric]] object playing an important role in [[discrete geometry]] and [[combinatorial commutative algebra]]. It is a [[polytope]] in a Euclidean space '''R'''<sup>n</sup> which is a [[convex hull]] of finitely many points in the [[integer lattice]] '''Z'''<sup>n</sup> ⊂ '''R'''<sup>n</sup>. Such objects are prominently featured in the theory of [[toric variety\|toric varieties]], where they correspond to polarized projective toric varieties.

			== Examples ==
			* An ''n''-dimensional [[simplex]] Δ in '''R'''<sup>n+1</sup> is the convex hull of ''n''+1 points that do not lie on a single affine hyperplane. The simplex is a convex lattice polytope if (and only if) the vertices have integral coordinates. The corresponding toric variety is the ''n''-dimensional [[projective space]] '''P'''<sup>n</sup>.
			* The [[unit cube]] in '''R'''<sup>n</sup>, whose vertices are the ''2''<sup>n</sup> points all of whose coordinates are ''0'' or ''1'', is a convex lattice polytope. The corresponding toric variety is the [[Segre embedding]] of the ''n''-fold product of the projective line '''P'''<sup>1</sup>.
			* In the special case of two-dimensional convex lattice polytopes in '''R'''<sup>2</sup>, they are also known as '''convex lattice polygons'''.
			* In [[algebraic geometry]], an important instance of lattice polytopes called the '''Newton polytopes''' are the convex hulls of the set <math>A</math> which consists of all the exponent vectors appearing in a collection of monomials. For example, consider the polynomial of the form <math>axy+bx^2+cy^5+d</math> with <math>a,b,c,d \neq 0</math> has a lattice equal to the triangle
			:<math>{\rm conv}(\{(1,1),(2,0),(0,5),(0,0)\}).\ </math>

			== See also ==

			* [[Normal polytope]]
			* [[Pick's theorem]]
			* [[Ehrhart polynomial]]
			* [[Integer points in convex polyhedra]]

			== References ==
			* Ezra Miller, [[Bernd Sturmfels]], ''Combinatorial commutative algebra''. Graduate Texts in Mathematics, 227. Springer-Verlag, New York, 2005. xiv+417 pp. ISBN 0-387-22356-8

			{{geometry-stub}}
			[[Category:Polytopes]]
			[[Category:Lattice points]]

207.134.142.6: /* Algorithm description */

2012-07-13T20:01:54Z

Algorithm description

New page

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