Generalized suffix tree - Revision history

en>Anurag.x.singh: Added external link for a C implementation of Generalized Suffix Tree for two strings

2014-11-17T19:26:19Z

Added external link for a C implementation of Generalized Suffix Tree for two strings

← Older revision		Revision as of 21:26, 17 November 2014
Line 1:		Line 1:
	In [[mathematics]], '''Belyi's theorem''' on [[algebraic curve]]s states that any [[non-singular]] algebraic curve ''C'', defined by [[algebraic number]] coefficients, represents a [[compact Riemann surface]] which is a [[ramified covering]] of the ~~[[Riemann sphere]], ramified at three points only~~.		Hello. Let me introduce the writer. Her title is Emilia Shroyer but it's not the most female title out there. To collect cash is what her family and her appreciate. Managing people is what I do and the wage has been truly satisfying. For a whilst she's been in South Dakota.<br><br>Also visit my website :: [http://wmazowiecku.pl/stay-yeast-infection-free-using-these-helpful-suggestions/ wmazowiecku.pl]

	~~This~~ is ~~a result of [[G. V. Belyi]] from 1979. At the time~~ it ~~was considered surprising, and it spurred Grothendieck to develop his theory of [[Dessin d~~'~~enfant\|dessins d'enfant]], which describes nonsingular algebraic curves over~~ the ~~algebraic numbers using combinatorial data~~.

	~~== Quotients of the upper half-plane ==~~
	~~It follows that the Riemann surface in question can be taken to be~~

	~~:''H''/Γ~~

	~~with ''H'' the [[upper half-plane]]~~ and ~~Γ of [[finite index]] in the [[modular group]], compactified by [[cusp (singularity)\|cusps]]~~. ~~Since~~ the ~~modular group~~ has ~~[[non-congruence subgroup]]s, it is ''not'' the conclusion that any such curve is a [[modular curve]]~~.

	~~== Belyi functions ==~~
	~~A '''Belyi function''' is~~ a ~~[[holomorphic map]] from a compact Riemann surface ''S'' to the [[complex projective line]] '''P''~~'<~~sup~~>1<~~/sup~~>~~('''C''') ramified only over three points, which after a [[Möbius transformation]] may be taken to be <math> \{0, 1, \infty\} </math>. Belyi functions may be described combinatorially by~~ [~~[Dessin_d'enfant\|dessins d'enfants]].~~

	Belyi functions and dessins d'enfants – but not Belyi's theorem – date at least to the work of [[Felix Klein]]; he used them in his {{Harv\|Klein\|1879}} to study an 11-fold cover of the complex projective line with monodromy group PSL(2,11).<ref>{{citation
	~~\| last = le Bruyn \| first = Lieven~~
	~~\| title = Klein’s dessins d’enfant and the buckyball~~
	~~\| year = 2008~~
	~~\| url =~~ http://~~www.neverendingbooks.org/index~~.~~php~~/~~kleins~~-~~dessins~~-~~denfant~~-~~and~~-~~the-buckyball.html}}.</ref>~~

	~~== Applications ==~~
	~~Belyi's theorem is an [[existence theorem]] for Belyi functions, and has subsequently been much used in the [[inverse Galois problem]].~~

	~~==References==~~
	~~{{reflist}}~~
	~~{{refbegin}}~~
	*[[J.-~~P. Serre\|Serre, J.~~-~~P.]] (1989), ''Lectures on the Mordell~~-~~Weil Theorem'', p. 71~~
	*{{cite doi\|10.1007/~~BF02086276}}~~
	*{{cite doi\|10.~~1070/IM1980v014n02ABEH001096}}~~
	~~{{refend}}~~

	~~==Further reading==~~
	* {{citation \| last1=Girondo \| first1=Ernesto \| last2=González-Diez \| first2=Gabino \| title=Introduction to compact Riemann surfaces and dessins d'enfants \| series=London Mathematical Society Student Texts \| volume=79 \| location=Cambridge \| publisher=[[Cambridge University Press]] \| year=2012 \| isbn=978-0-521-74022-7 \| zbl=1253.30001 }}
	* {{citation \| editor1=Dorian Goldfeld \| editor2=Jay Jorgenson \| editor3=Peter Jones \| editor4=Dinakar Ramakrishnan \| editor5=Kenneth A. Ribet \| editor6=John Tate \| title=Number Theory, Analysis and Geometry. In Memory of Serge Lang \| publisher=Springer \| year=2012 \| isbn=978-1-4614-1259-5 \| author=Wushi Goldring \| chapter=Unifying themes suggested by Belyi's Theorem \| pages=181–214 }}

	~~[[Category:Algebraic curves]]~~
	~~[[Category:Theorems in algebraic geometry]~~]

en>Nodirt: Fixed a typo: generalised -> generalized

2013-10-03T00:30:05Z

Fixed a typo: generalised -> generalized

← Older revision		Revision as of 02:30, 3 October 2013
Line 1:		Line 1:
	~~The~~ [~~http://c~~-~~batang~~.co.~~kr/?document_srl~~=~~485588&mid~~=~~levelup_board http~~://c-~~batang~~.co.~~kr/?document_srl~~=~~485588&mid~~=~~levelup_board~~] ~~name~~ ~~home std test of the writer is Figures~~ but it's ~~not~~ the ~~most~~ ~~at home std testing [~~http://~~dermatology~~.~~About~~.~~com~~/od/~~dermphotos/ig/Herpes~~-~~Gallery~~/ ~~masucline~~] ~~name out there~~. ~~In her professional life she is a payroll clerk but~~ [~~http:~~/~~/riddlesandpoetry~~.~~com~~/?q=~~node/19209 std testing at home~~] ~~she's usually wanted her own company~~. ~~One of the very very best things in the globe for him is to collect badges but he is having difficulties to discover time for it~~. ~~Years ago he moved to North Dakota~~ and ~~his family enjoys it~~.~~<br><br>Here is my webpage;~~ [~~http~~:~~//www.fuguporn.com/user/RMitchell at home std testing~~]		In [[mathematics]], '''Belyi's theorem''' on [[algebraic curve]]s states that any [[non-singular]] algebraic curve ''C'', defined by [[algebraic number]] coefficients, represents a [[compact Riemann surface]] which is a [[ramified covering]] of the [[Riemann sphere]], ramified at three points only.

			This is a result of [[G. V. Belyi]] from 1979. At the time it was considered surprising, and it spurred Grothendieck to develop his theory of [[Dessin d'enfant\|dessins d'enfant]], which describes nonsingular algebraic curves over the algebraic numbers using combinatorial data.

			== Quotients of the upper half-plane ==
			It follows that the Riemann surface in question can be taken to be

			:''H''/Γ

			with ''H'' the [[upper half-plane]] and Γ of [[finite index]] in the [[modular group]], compactified by [[cusp (singularity)\|cusps]]. Since the modular group has [[non-congruence subgroup]]s, it is ''not'' the conclusion that any such curve is a [[modular curve]].

			== Belyi functions ==
			A '''Belyi function''' is a [[holomorphic map]] from a compact Riemann surface ''S'' to the [[complex projective line]] '''P'''<sup>1</sup>('''C''') ramified only over three points, which after a [[Möbius transformation]] may be taken to be <math> \{0, 1, \infty\} </math>. Belyi functions may be described combinatorially by [[Dessin_d'enfant\|dessins d'enfants]].

			Belyi functions and dessins d'enfants – but not Belyi's theorem – date at least to the work of [[Felix Klein]]; he used them in his {{Harv\|Klein\|1879}} to study an 11-fold cover of the complex projective line with monodromy group PSL(2,11).<ref>{{citation
			\| last = le Bruyn \| first = Lieven
			\| title = Klein’s dessins d’enfant and the buckyball
			\| year = 2008
			\| url = http://www.neverendingbooks.org/index.php/kleins-dessins-denfant-and-the-buckyball.html}}.</ref>

			== Applications ==
			Belyi's theorem is an [[existence theorem]] for Belyi functions, and has subsequently been much used in the [[inverse Galois problem]].

			==References==
			{{reflist}}
			{{refbegin}}
			*[[J.-P. Serre\|Serre, J.-P.]] (1989), ''Lectures on the Mordell-Weil Theorem'', p. 71
			*{{cite doi\|10.1007/BF02086276}}
			*{{cite doi\|10.1070/IM1980v014n02ABEH001096}}
			{{refend}}

			==Further reading==
			* {{citation \| last1=Girondo \| first1=Ernesto \| last2=González-Diez \| first2=Gabino \| title=Introduction to compact Riemann surfaces and dessins d'enfants \| series=London Mathematical Society Student Texts \| volume=79 \| location=Cambridge \| publisher=[[Cambridge University Press]] \| year=2012 \| isbn=978-0-521-74022-7 \| zbl=1253.30001 }}
			* {{citation \| editor1=Dorian Goldfeld \| editor2=Jay Jorgenson \| editor3=Peter Jones \| editor4=Dinakar Ramakrishnan \| editor5=Kenneth A. Ribet \| editor6=John Tate \| title=Number Theory, Analysis and Geometry. In Memory of Serge Lang \| publisher=Springer \| year=2012 \| isbn=978-1-4614-1259-5 \| author=Wushi Goldring \| chapter=Unifying themes suggested by Belyi's Theorem \| pages=181–214 }}

			[[Category:Algebraic curves]]
			[[Category:Theorems in algebraic geometry]]

en>Ninjagecko: Ninjagecko moved page Generalised suffix tree to Generalized suffix tree over redirect: More correctly spelled "generalized" (not "generalised") by factor of 10, only comment on Talk page agrees. This process will leave redirect.

2012-05-24T19:19:02Z

Ninjagecko moved page Generalised suffix tree to Generalized suffix tree over redirect: More correctly spelled "generalized" (not "generalised") by factor of 10, only comment on Talk page agrees. This process will leave redirect.

New page

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