InforLorV4, PascalFrancis, Corpus, bibRecord, 000A59

Counting rooted maps on a surface

Identifieur interne : 000A59 ( PascalFrancis/Corpus ); précédent : 000A58; suivant : 000A60

Counting rooted maps on a surface

Auteurs : D. Arques ; A. Giorgetti

Source :

Theoretical computer science [ 0304-3975 ] ; 2000.

RBID : Pascal:00-0169830

Descripteurs français

Pascal (Inist)
- Enumération, Série exponentielle, Série formelle, Surface Riemann, Equation fonctionnelle, Théorème unicité, Topologie algébrique, Orientabilité, Série exponentielle formelle, Bouteille Klein, Application à racine.

English descriptors

KwdEn :
- Algebraic topology, Enumeration, Formal power series, Formal series, Functional equation, Klein bottle, Orientability, Power series, Riemann surface, Rooted tree, Uniqueness theorem.

Abstract

Several enumeration results are known about rooted maps on orientable surfaces, whereas rooted maps on non-orientable surfaces have seldom been studied. First, we unify both kind of maps, giving general functional equations for the generating series which counts rooted maps on any locally orientable surface, by number of vertices and faces. Then, we formally solve these equations, in order to establish a detailed common formula for all these generating series. All of them appear to be algebraic functions of the variables counting the number of vertices and faces. Explicit expressions and numerical tables for the series counting rooted maps on the non-orientable surfaces of genus 3 and 4 are given.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A02	`01`			`@0 TCSCDI`
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A06				`@2 1-2`
A08	`01`	`1`	`ENG`	`@1 Counting rooted maps on a surface`
A11	`01`	`1`		`@1 ARQUES (D.)`
A11	`02`	`1`		`@1 GIORGETTI (A.)`
A14	`01`			`@1 Institut Gaspard Monge, Université de Marne la Vallée, 5, boulevard Descartes, Champs sur Marne @2 77454 Marne la Vallée @3 FRA @Z 1 aut.`
A14	`02`			`@1 LORIA, Université Henri Poincaré, Nancy I, Domaine scientifique Victor Grignard, B. P. 239 @2 54506 Vandœuvre les Nancy @3 FRA @Z 2 aut.`
A20				`@1 255-272`
A21				`@1 2000`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 17243 @5 354000086807540110`
A44				`@0 0000 @1 © 2000 INIST-CNRS. All rights reserved.`
A45				`@0 16 ref.`
A47	`01`	`1`		`@0 00-0169830`
A60				`@1 P`
A61				`@0 A`
A64	`01`	`1`		`@0 Theoretical computer science`
A66	`01`			`@0 NLD`
C01	`01`		`ENG`	@0 Several enumeration results are known about rooted maps on orientable surfaces, whereas rooted maps on non-orientable surfaces have seldom been studied. First, we unify both kind of maps, giving general functional equations for the generating series which counts rooted maps on any locally orientable surface, by number of vertices and faces. Then, we formally solve these equations, in order to establish a detailed common formula for all these generating series. All of them appear to be algebraic functions of the variables counting the number of vertices and faces. Explicit expressions and numerical tables for the series counting rooted maps on the non-orientable surfaces of genus 3 and 4 are given.
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C03	`01`	`X`	`ENG`	`@0 Enumeration @5 01`
C03	`01`	`X`	`SPA`	`@0 Enumeración @5 01`
C03	`02`	`3`	`FRE`	`@0 Série exponentielle @5 02`
C03	`02`	`3`	`ENG`	`@0 Power series @5 02`
C03	`03`	`X`	`FRE`	`@0 Série formelle @5 03`
C03	`03`	`X`	`ENG`	`@0 Formal series @5 03`
C03	`03`	`X`	`SPA`	`@0 Serie formal @5 03`
C03	`04`	`X`	`FRE`	`@0 Surface Riemann @5 04`
C03	`04`	`X`	`ENG`	`@0 Riemann surface @5 04`
C03	`04`	`X`	`SPA`	`@0 Superficie Riemann @5 04`
C03	`05`	`X`	`FRE`	`@0 Equation fonctionnelle @5 05`
C03	`05`	`X`	`ENG`	`@0 Functional equation @5 05`
C03	`05`	`X`	`SPA`	`@0 Ecuación funcional @5 05`
C03	`06`	`X`	`FRE`	`@0 Théorème unicité @5 06`
C03	`06`	`X`	`ENG`	`@0 Uniqueness theorem @5 06`
C03	`06`	`X`	`SPA`	`@0 Teorema unicidad @5 06`
C03	`07`	`X`	`FRE`	`@0 Topologie algébrique @5 07`
C03	`07`	`X`	`ENG`	`@0 Algebraic topology @5 07`
C03	`07`	`X`	`SPA`	`@0 Topología algebraica @5 07`
C03	`08`	`X`	`FRE`	`@0 Orientabilité @4 CD @5 96`
C03	`08`	`X`	`ENG`	`@0 Orientability @4 CD @5 96`
C03	`09`	`X`	`FRE`	`@0 Série exponentielle formelle @4 CD @5 97`
C03	`09`	`X`	`ENG`	`@0 Formal power series @4 CD @5 97`
C03	`10`	`X`	`FRE`	`@0 Bouteille Klein @4 CD @5 98`
C03	`10`	`X`	`ENG`	`@0 Klein bottle @4 CD @5 98`
C03	`11`	`X`	`FRE`	`@0 Application à racine @4 CD @5 99`
C03	`11`	`X`	`ENG`	`@0 Rooted tree @4 CD @5 99`
N21				`@1 122`

Format Inist (serveur)

NO :	PASCAL 00-0169830 INIST
ET :	Counting rooted maps on a surface
AU :	ARQUES (D.); GIORGETTI (A.)
AF :	Institut Gaspard Monge, Université de Marne la Vallée, 5, boulevard Descartes, Champs sur Marne/77454 Marne la Vallée/France (1 aut.); LORIA, Université Henri Poincaré, Nancy I, Domaine scientifique Victor Grignard, B. P. 239/54506 Vandœuvre les Nancy/France (2 aut.)
DT :	Publication en série; Niveau analytique
SO :	Theoretical computer science; ISSN 0304-3975; Coden TCSCDI; Pays-Bas; Da. 2000; Vol. 234; No. 1-2; Pp. 255-272; Bibl. 16 ref.
LA :	Anglais
EA :	Several enumeration results are known about rooted maps on orientable surfaces, whereas rooted maps on non-orientable surfaces have seldom been studied. First, we unify both kind of maps, giving general functional equations for the generating series which counts rooted maps on any locally orientable surface, by number of vertices and faces. Then, we formally solve these equations, in order to establish a detailed common formula for all these generating series. All of them appear to be algebraic functions of the variables counting the number of vertices and faces. Explicit expressions and numerical tables for the series counting rooted maps on the non-orientable surfaces of genus 3 and 4 are given.
CC :	001A02G02; 001A02B01A; 001A02C02
FD :	Enumération; Série exponentielle; Série formelle; Surface Riemann; Equation fonctionnelle; Théorème unicité; Topologie algébrique; Orientabilité; Série exponentielle formelle; Bouteille Klein; Application à racine
ED :	Enumeration; Power series; Formal series; Riemann surface; Functional equation; Uniqueness theorem; Algebraic topology; Orientability; Formal power series; Klein bottle; Rooted tree
SD :	Enumeración; Serie formal; Superficie Riemann; Ecuación funcional; Teorema unicidad; Topología algebraica
LO :	INIST-17243.354000086807540110
ID :	00-0169830

Links to Exploration step

Pascal:00-0169830

Le document en format XML

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<ET>Counting rooted maps on a surface</ET>
<AU>ARQUES (D.); GIORGETTI (A.)</AU>
<AF>Institut Gaspard Monge, Université de Marne la Vallée, 5, boulevard Descartes, Champs sur Marne/77454 Marne la Vallée/France (1 aut.); LORIA, Université Henri Poincaré, Nancy I, Domaine scientifique Victor Grignard, B. P. 239/54506 Vandœuvre les Nancy/France (2 aut.)</AF>
<DT>Publication en série; Niveau analytique</DT>
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<LA>Anglais</LA>
<EA>Several enumeration results are known about rooted maps on orientable surfaces, whereas rooted maps on non-orientable surfaces have seldom been studied. First, we unify both kind of maps, giving general functional equations for the generating series which counts rooted maps on any locally orientable surface, by number of vertices and faces. Then, we formally solve these equations, in order to establish a detailed common formula for all these generating series. All of them appear to be algebraic functions of the variables counting the number of vertices and faces. Explicit expressions and numerical tables for the series counting rooted maps on the non-orientable surfaces of genus 3 and 4 are given.</EA>
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Counting rooted maps on a surface

Counting rooted maps on a surface

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