From Christoffel Words to Markoff Numbers
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From Christoffel Words to Markoff Numbers
Reutenauer, Christophe
Oxford University Press
11/2018
170
Dura
Inglês
9780198827542
15 a 20 dias
434
Descrição não disponível.
The Theory of Markoff
1: Basics
2: Words
2.1: Tiling the plane with a parallelogram
2.2: Christoffel words
2.3: Palindromes
2.4: Standard factorization
2.5: The tree of Christoffel pairs
2.6: Sturmian morphisms
3: Markoff numbers
3.1: Markoff triples and numbers
3.2: The tree of Markoff triples
3.3: The Markoff injectivity conjecture
4: The Markoff property
4.1: Markoff property for infinite words
4.2: Markoff property for bi-infinite words
5: Continued fractions
5.1: Finite continued fractions
5.2: Infinite continued fractions
5.3: Periodic expansions yield quadratic numbers
5.4: Approximations of real numbers
5.5: Lagrange number of a real number
5.6: Ordering continued fractions
6: Words and quadratic numbers
6.1: Continued fractions associated to Christoffel words
6.2: Marko supremum of a bi-innite sequence
6.3: Lagrange number of a sequence
7: Lagrange numbers less than 3
7.1: From L(s) < 3 to the Marko property
7.2: Bi-infinite sequences
8: Markoff's theorem for approximations
8.1: Main lemma
8.2: Markoff's theorem for approximations
8.3: Good and bad approximations
9: Markoff's theorem for quadratic forms
9.1: Indefinite real binary quadratic forms
9.2: Infimum
9.3: Markoff's theorem for quadratic forms
10: Numerology
10.1: Thirteen Markoff numbers
10.2: The golden ratio and other numbers
10.3: The matrices U(w) and Frobenius congruences
10.4: Markoff quadratic forms
11: Historical notes
The Theory of Christoel Words
12: Palindromes and periods
12.1: Palindromes
12.2: Periods
13: Lyndon words and Christoffel words
13.1: Slopes
13.2: Lyndon words
13.3: Maximal Lyndon words
13.4: Unbordered Sturmian words
13.5: Equilibrated Lyndon words
14: Stern-Brocot tree
14.1: The tree of Christoffel words
14.2: Stern-Brocot tree and continued fractions
14.3: The Raney tree and dual words
14.4: Convex hull
15: Conjugates and factors
15.1: Cayley graph
15.2: Conjugates
15.3: Factors
15.4: Palindromes again
15.5: Finite Sturmian words
16: Free group on two generators
16.1: Bases and automorphisms
16.2: Inner automorphisms
16.3: Christoffel bases
16.4: Nielsen's criterion
16.5: An algorithm for the bases
16.6: Sturmian morphisms again
17: Complements
17.1: Other results on Christoffel words
17.2: Lyndon words and Lie theory
17.3: Music
1: Basics
2: Words
2.1: Tiling the plane with a parallelogram
2.2: Christoffel words
2.3: Palindromes
2.4: Standard factorization
2.5: The tree of Christoffel pairs
2.6: Sturmian morphisms
3: Markoff numbers
3.1: Markoff triples and numbers
3.2: The tree of Markoff triples
3.3: The Markoff injectivity conjecture
4: The Markoff property
4.1: Markoff property for infinite words
4.2: Markoff property for bi-infinite words
5: Continued fractions
5.1: Finite continued fractions
5.2: Infinite continued fractions
5.3: Periodic expansions yield quadratic numbers
5.4: Approximations of real numbers
5.5: Lagrange number of a real number
5.6: Ordering continued fractions
6: Words and quadratic numbers
6.1: Continued fractions associated to Christoffel words
6.2: Marko supremum of a bi-innite sequence
6.3: Lagrange number of a sequence
7: Lagrange numbers less than 3
7.1: From L(s) < 3 to the Marko property
7.2: Bi-infinite sequences
8: Markoff's theorem for approximations
8.1: Main lemma
8.2: Markoff's theorem for approximations
8.3: Good and bad approximations
9: Markoff's theorem for quadratic forms
9.1: Indefinite real binary quadratic forms
9.2: Infimum
9.3: Markoff's theorem for quadratic forms
10: Numerology
10.1: Thirteen Markoff numbers
10.2: The golden ratio and other numbers
10.3: The matrices U(w) and Frobenius congruences
10.4: Markoff quadratic forms
11: Historical notes
The Theory of Christoel Words
12: Palindromes and periods
12.1: Palindromes
12.2: Periods
13: Lyndon words and Christoffel words
13.1: Slopes
13.2: Lyndon words
13.3: Maximal Lyndon words
13.4: Unbordered Sturmian words
13.5: Equilibrated Lyndon words
14: Stern-Brocot tree
14.1: The tree of Christoffel words
14.2: Stern-Brocot tree and continued fractions
14.3: The Raney tree and dual words
14.4: Convex hull
15: Conjugates and factors
15.1: Cayley graph
15.2: Conjugates
15.3: Factors
15.4: Palindromes again
15.5: Finite Sturmian words
16: Free group on two generators
16.1: Bases and automorphisms
16.2: Inner automorphisms
16.3: Christoffel bases
16.4: Nielsen's criterion
16.5: An algorithm for the bases
16.6: Sturmian morphisms again
17: Complements
17.1: Other results on Christoffel words
17.2: Lyndon words and Lie theory
17.3: Music
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
The Theory of Markoff
1: Basics
2: Words
2.1: Tiling the plane with a parallelogram
2.2: Christoffel words
2.3: Palindromes
2.4: Standard factorization
2.5: The tree of Christoffel pairs
2.6: Sturmian morphisms
3: Markoff numbers
3.1: Markoff triples and numbers
3.2: The tree of Markoff triples
3.3: The Markoff injectivity conjecture
4: The Markoff property
4.1: Markoff property for infinite words
4.2: Markoff property for bi-infinite words
5: Continued fractions
5.1: Finite continued fractions
5.2: Infinite continued fractions
5.3: Periodic expansions yield quadratic numbers
5.4: Approximations of real numbers
5.5: Lagrange number of a real number
5.6: Ordering continued fractions
6: Words and quadratic numbers
6.1: Continued fractions associated to Christoffel words
6.2: Marko supremum of a bi-innite sequence
6.3: Lagrange number of a sequence
7: Lagrange numbers less than 3
7.1: From L(s) < 3 to the Marko property
7.2: Bi-infinite sequences
8: Markoff's theorem for approximations
8.1: Main lemma
8.2: Markoff's theorem for approximations
8.3: Good and bad approximations
9: Markoff's theorem for quadratic forms
9.1: Indefinite real binary quadratic forms
9.2: Infimum
9.3: Markoff's theorem for quadratic forms
10: Numerology
10.1: Thirteen Markoff numbers
10.2: The golden ratio and other numbers
10.3: The matrices U(w) and Frobenius congruences
10.4: Markoff quadratic forms
11: Historical notes
The Theory of Christoel Words
12: Palindromes and periods
12.1: Palindromes
12.2: Periods
13: Lyndon words and Christoffel words
13.1: Slopes
13.2: Lyndon words
13.3: Maximal Lyndon words
13.4: Unbordered Sturmian words
13.5: Equilibrated Lyndon words
14: Stern-Brocot tree
14.1: The tree of Christoffel words
14.2: Stern-Brocot tree and continued fractions
14.3: The Raney tree and dual words
14.4: Convex hull
15: Conjugates and factors
15.1: Cayley graph
15.2: Conjugates
15.3: Factors
15.4: Palindromes again
15.5: Finite Sturmian words
16: Free group on two generators
16.1: Bases and automorphisms
16.2: Inner automorphisms
16.3: Christoffel bases
16.4: Nielsen's criterion
16.5: An algorithm for the bases
16.6: Sturmian morphisms again
17: Complements
17.1: Other results on Christoffel words
17.2: Lyndon words and Lie theory
17.3: Music
1: Basics
2: Words
2.1: Tiling the plane with a parallelogram
2.2: Christoffel words
2.3: Palindromes
2.4: Standard factorization
2.5: The tree of Christoffel pairs
2.6: Sturmian morphisms
3: Markoff numbers
3.1: Markoff triples and numbers
3.2: The tree of Markoff triples
3.3: The Markoff injectivity conjecture
4: The Markoff property
4.1: Markoff property for infinite words
4.2: Markoff property for bi-infinite words
5: Continued fractions
5.1: Finite continued fractions
5.2: Infinite continued fractions
5.3: Periodic expansions yield quadratic numbers
5.4: Approximations of real numbers
5.5: Lagrange number of a real number
5.6: Ordering continued fractions
6: Words and quadratic numbers
6.1: Continued fractions associated to Christoffel words
6.2: Marko supremum of a bi-innite sequence
6.3: Lagrange number of a sequence
7: Lagrange numbers less than 3
7.1: From L(s) < 3 to the Marko property
7.2: Bi-infinite sequences
8: Markoff's theorem for approximations
8.1: Main lemma
8.2: Markoff's theorem for approximations
8.3: Good and bad approximations
9: Markoff's theorem for quadratic forms
9.1: Indefinite real binary quadratic forms
9.2: Infimum
9.3: Markoff's theorem for quadratic forms
10: Numerology
10.1: Thirteen Markoff numbers
10.2: The golden ratio and other numbers
10.3: The matrices U(w) and Frobenius congruences
10.4: Markoff quadratic forms
11: Historical notes
The Theory of Christoel Words
12: Palindromes and periods
12.1: Palindromes
12.2: Periods
13: Lyndon words and Christoffel words
13.1: Slopes
13.2: Lyndon words
13.3: Maximal Lyndon words
13.4: Unbordered Sturmian words
13.5: Equilibrated Lyndon words
14: Stern-Brocot tree
14.1: The tree of Christoffel words
14.2: Stern-Brocot tree and continued fractions
14.3: The Raney tree and dual words
14.4: Convex hull
15: Conjugates and factors
15.1: Cayley graph
15.2: Conjugates
15.3: Factors
15.4: Palindromes again
15.5: Finite Sturmian words
16: Free group on two generators
16.1: Bases and automorphisms
16.2: Inner automorphisms
16.3: Christoffel bases
16.4: Nielsen's criterion
16.5: An algorithm for the bases
16.6: Sturmian morphisms again
17: Complements
17.1: Other results on Christoffel words
17.2: Lyndon words and Lie theory
17.3: Music
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
