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1.

図書

図書
Miklós Bóna
出版情報: River Edge, N.J. : World Scientific, c2002  xvii, 406 p. ; 24 cm
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2.

図書

図書
V.N. Sachkov, V.E. Tarakanov ; translated by Valentin F. Kolchin
出版情報: Providence, R.I. : American Mathematical Society, c2002  ix, 269 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 213
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Matrices and Configurations
Ryser classes
Nonnegative matrices and extremal combinatorial problems
Asymptotic methods in the study of nonnegative matrices
Totally indecomposable, chainable, and prime matrices
Sequences of nonnegative matrices
Bibliography
Index
Matrices and Configurations
Ryser classes
Nonnegative matrices and extremal combinatorial problems
3.

図書

図書
M. Lothaire
出版情報: Cambridge : Cambridge University Press, 2002  xiii, 504 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 90
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Preface
Finite and Infinite Words / Chapter 1:
Introduction / 1.0:
Semigroups / 1.1:
Words / 1.2:
Automata / 1.3:
Generating series / 1.4:
Symbolic dynamical systems / 1.5:
Unavoidable sets / 1.6:
Problems
Notes
Sturmian Words / Chapter 2:
Equivalent definitions / 2.0:
Standard words / 2.2:
Sturmian morphisms / 2.3:
Unavoidable Patterns / Chapter 3:
Definitions and basic properties / 3.0:
Deciding avoidability: the Zimin algorithm / 3.2:
Avoidability on a fixed alphabet / 3.3:
Sesquipowers / Chapter 4:
Bi-ideal sequences / 4.0:
Canonical factorizations / 4.2:
Sesquipowers and recurrence / 4.3:
Extensions of a theorem of Shirshov / 4.4:
Finiteness conditions for semigroups / 4.5:
The Plactic Monoid / Chapter 5:
Schensted's algorithm / 5.0:
Greene's invariants and the plactic monoid / 5.2:
The Robinson--Schensted--Knuth correspondence / 5.3:
Schur functions and the Littlewood--Richardson rule / 5.4:
Coplactic operations / 5.5:
Cyclage and canonical embeddings / 5.6:
Codes / Chapter 6:
X-factorizations / 6.0:
Defect / 6.2:
More defect / 6.3:
A theorem of Schutzenberger / 6.4:
Numeration Systems / Chapter 7:
Standard representation of numbers / 7.0:
Beta-expansions / 7.2:
U-representations / 7.3:
Representation of complex numbers / 7.4:
Periodicity / Chapter 8:
Periods in a finite word / 8.0:
Local versus global periodicity / 8.2:
Infinite words / 8.3:
Centralizers of Noncommutative Series and Polynomials / Chapter 9:
Cohn's centralizer theorem / 9.0:
Euclidean division and principal right ideals / 9.2:
Integral closure of the centralizer / 9.3:
Homomorphisms into k[t] / 9.4:
Bergman's centralizer theorem / 9.5:
Free subalgebras and the defect theorem / 9.6:
Appendix: some commutative algebra / 9.7:
Transformations on Words and q-Calculus / Chapter 10:
The q-binomial coefficients / 10.0:
The MacMahon Verfahren / 10.2:
The insertion technique / 10.3:
The (t, q)-factorial generating functions / 10.4:
Words and biwords / 10.5:
Commutations / 10.6:
The two commutations / 10.7:
The main algorithm / 10.8:
The inverse of the algorithm / 10.9:
Statistics on circuits / 10.10:
Statistics on words and equidistribution properties / 10.11:
Statistics on Permutations and Words / Chapter 11:
Preliminaries / 11.0:
Words with a given shape / 11.2:
Backsteps of permutations with a given shape / 11.3:
Inversions of permutations with a given shape / 11.4:
Lyndon factorization and cycles of permutations / 11.5:
Major index of permutations with a given cyclic type / 11.6:
Makanin's Algorithm / Chapter 12:
Words and word equations / 12.0:
The exponent of periodicity / 12.2:
Boundary equations / 12.3:
Proof of Theorem 12.3.10 / 12.4:
Independent Systems of Equations / Chapter 13:
Sets and equations / 13.0:
The compactness property / 13.2:
Independence of finite systems of equations / 13.3:
Semigroups without the compactness property / 13.4:
Semigroups with the compactness property / 13.5:
References
Index of Notation
General Index
Preface
Finite and Infinite Words / Chapter 1:
Introduction / 1.0:
4.

図書

図書
Victor M. Buchstaber, Taras E. Panov
出版情報: Providence, R.I. : American Mathematical Society, c2002  viii, 144 p. ; 26 cm
シリーズ名: University lecture series ; 24
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Introduction
Polytopes Topology and combinatorics of simplicial complexes
Commutative and homological algebra of simplicial complexes
Cubical complexes Toric and quasitoric manifolds
Moment-angle complexes Cohomology of moment-angle complexes and combinatorics of triangulated manifolds
Cohomology rings of subspace arrangement complements
Bibliography
Index
Introduction
Polytopes Topology and combinatorics of simplicial complexes
Commutative and homological algebra of simplicial complexes
5.

図書

図書
edited by J.W.P. Hirschfeld
出版情報: Cambridge ; New York : Cambridge University Press, 2001  x, 301 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 288
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Crispin / Nash-Williams J. Sheehan1:
The Penrose polynomial of graphs and matroids / M. Aigner2:
Cyclic designs / I. Anderson3:
Orthogonal designs and space-time codes for wireless communication / A. R. Calderbank ; A. F. Naguib4:
Sampling and counting unlabelled structures / L. A. Goldberg5:
Graphs on surfaces and graph minors / B. Mohar6:
Graph colouring with the probabilistic method / M. S. O. Molloy7:
The interplay between graphs and matroids / J. G. Oxley8:
Ovoids, spreads and m-systems of finite classical polar spaces / J. A. Thas9:
List colourings of graphs / D. R. Woodall10:
Crispin / Nash-Williams J. Sheehan1:
The Penrose polynomial of graphs and matroids / M. Aigner2:
Cyclic designs / I. Anderson3:
6.

図書

図書
Stasys Jukna
出版情報: Berlin ; New York : Springer, c2001  xvii, 375 p. ; 24 cm
シリーズ名: Texts in theoretical computer science ; An EATCS series
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Introduction
The Classis: Counting / I:
The Pigeon-Hole Principle
Principle of Inclusion and Exclusion
Systems of Distinct Representatives
Colorings
Chains and Antichains
Intersecting Families
Covers and Transversals
Sunflowers
Density and Universality
Designs
Witness Sets
Isolation Lemmas
The Linear Algebra Method: Basic Method / II:
The Polynomial Technique
Monotone Span Programs
The Probabilistic Method: Basic Tools / III:
Counting Sieve
Lovàsz Sieve
Linearity of Expectation
The Deletion Method
Second Moment Method
Bounding of Large Deviations
Randomized Algorithms
Derandomization
The Entropy Function
Random Walks and Search Problems
Fragments of Ramsey Theory: Ramsey's Theorem / IV:
The Hales-Jewett Theorem
Epilogue: What Next?
Bibliography
Index
Introduction
The Classis: Counting / I:
The Pigeon-Hole Principle
7.

図書

図書
by Percy A. MacMahon
出版情報: Cambridge : Cambridge University Press, 1915-1916  2 v. ; 27 cm
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8.

図書

図書
Dominique Foata, Guo-Niu Han (eds.)
出版情報: Berlin ; Heidelberg ; New York : Springer-Verlag, c2001  vii, 426 p. ; 24 cm
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9.

図書

図書
Andreas Dress ... [et al.]
出版情報: Cambridge [England] : Cambridge University Press, 2012  xii, 264 p. ; 24 cm
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Preface
Preliminaries / 1:
Sets, set systems, and partially ordered sets / 1.1:
Graphs / 1.2:
Metric spaces / 1.3:
Computational complexity / 1.4:
Encoding X-trees / 2:
X-trees / 2.1:
Encoding X-trees with splits / 2.2:
Encoding X-trees with metrics / 2.3:
Encoding X-trees with quartets / 2.4:
Consistency of X-tree encodings / 3:
The 4-point condition / 3.1:
Compatibility / 3.2:
Quartet systems / 3.3:
From split systems to networks / 4:
The Buneman graph / 4.1:
The Buneman graph of a compatible split system / 4.2:
Median networks / 4.3:
Split networks / 4.4:
Split graphs and metrics: The theory of X-nets / 4.5:
From metrics to networks: The tight span / 5:
The tight span / 5.1:
A canonical contraction from P(D) onto T(D) / 5.2:
The tight span of a finite metric space / 5.3:
Networks from tight spans / 5.4:
Network realizations of metrics / 5.5:
Optimal and hereditarily optimal realizations / 5.6:
From quartet and tree systems to trees / 6:
On quartet systems / 6.1:
On set and tree systems / 6.2:
Constructing trees from quartet, tree, and set systems / 6.3:
Slim tree systems / 6.4:
Definitive set systems / 6.5:
From metrics to split systems and back / 7:
Buneman splits / 7.1:
Weakly compatible split systems / 7.2:
From weighted split systems to bivariate maps / 7.3:
The Buneman complex and the tight span / 7.4:
Maps to and from quartet systems / 8:
A Galois connection between split and quartet systems / 8.1:
A map from quartets to metrics / 8.2:
Transitive quartet systems / 8.3:
Rooted trees and the Farris transform / 9:
Rooted X-trees, clusters, and triplets / 9.1:
Dated rooted X-trees and hierarchical dissimilarities / 9.2:
Affine versus projective clustering and the combinatorial Farris transform / 9.3:
Hierarchical dissimilarities, hyperbolic maps, and their Farris transform / 9.4:
Hierarchical dissimilarities, generalized metrics, and the tight-span construction / 9.5:
Algorithmic issues / 9.6:
On measuring and removing inconsistencies / 10:
k-compatibility / 10.1:
A-hierarchical approximations / 10.2:
Quartet-Joining and QNet / 10.3:
Commonly used symbols
Bibliography
Index
Preface
Preliminaries / 1:
Sets, set systems, and partially ordered sets / 1.1:
10.

図書

図書
R.B.J.T. Allenby, Alan Slomson
出版情報: Boca Raton, Fla. : CRC Press, c2011  xv, 430 p. ; 26 cm
シリーズ名: Discrete mathematics and its applications / Kenneth H. Rosen, series editor
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Preface to the Second Edition
Acknowledgments
Authors
What's it All About? / Chapter 1:
What is Combinatorics? / 1.1:
Classic Problems / 1.2:
What You Need to Know / 1.3:
Are you Sitting Comfortably? / 1.4:
Permutations and Combinations / Chapter 2:
The Combinatorial Approach / 2.1:
Permutations / 2.2:
Combinations / 2.3:
Applications to Probability Problems / 2.4:
The Multinomial Theorem / 2.5:
Permutations and Cycles / 2.6:
Occupancy Problems / Chapter 3:
Counting the Solutions of Equations / 3.1:
New Problems from Old / 3.2:
A "Reduction" Theorem for the Stirling Numbers / 3.3:
The Inclusion-Exclusion Principle / Chapter 4:
Double Counting / 4.1:
Derangements / 4.2:
A Formula for the Stirling Numbers / 4.3:
Stirling and Catalan Numbers / Chapter 5:
Stirling Numbers / 5.1:
Permutations and Stirling Numbers / 5.2:
Catalan Numbers / 5.3:
Partitions and Dot Diagrams / Chapter 6:
Partitions / 6.1:
Dot Diagrams / 6.2:
A Bit of Speculation / 6.3:
More Proofs Using Dot Diagrams / 6.4:
Generating Functions and Recurrence Relations / Chapter 7:
Functions and Power Series / 7.1:
Generating Functions / 7.2:
What is a Recurrence Relation? / 7.3:
Fibonacci Numbers / 7.4:
Solving Homogeneous Linear Recurrence Relations / 7.5:
Nonhomogeneous Linear Recurrence Relations / 7.6:
The Theory of Linear Recurrence Relations / 7.7:
Some Nonlinear Recurrence Relations / 7.8:
Partitions and Generating Functions / Chapter 8:
The Generating Function for the Partition Numbers / 8.1:
A Quick(ish) Way of Finding p(n) / 8.2:
An Upper Bound for the Partition Numbers / 8.3:
The Hardy-Ramanujan Formula / 8.4:
The Story of Hardy and Ramanujan / 8.5:
Introduction to Graphs / Chapter 9:
Graphs and Pictures / 9.1:
Graphs: A Picture-Free Definition / 9.2:
Isomorphism of Graphs / 9.3:
Paths and Connected Graphs / 9.4:
Planar Graphs / 9.5:
Eulerian Graphs / 9.6:
Hamiltonian Graphs / 9.7:
The Four-Color Theorem / 9.8:
Trees / Chapter 10:
What is a Tree? / 10.1:
Labeled Trees / 10.2:
Spanning Trees and Minimal Connectors / 10.3:
The Shortest-Path Problem / 10.4:
Groups of Permutations / Chapter 11:
Permutations as Groups / 11.1:
Symmetry Groups / 11.2:
Subgroups and Lagrange's Theorem / 11.3:
Orders of Group Elements / 11.4:
The Orders of Permutations / 11.5:
Group Actions / Chapter 12:
Colorings / 12.1:
The Axioms for Group Actions / 12.2:
Orbits / 12.3:
Stabilizers / 12.4:
Counting Patterns / Chapter 13:
Frobenius's Counting Theorem / 13.1:
Applications of Frobenius's Counting Theorem / 13.2:
Pólya Counting / Chapter 14:
Colorings and Group Actions / 14.1:
Pattern Inventories / 14.2:
The Cycle Index of a Group / 14.3:
Pólya's Counting Theorem: Statement and Examples / 14.4:
Pólya's Counting Theorem: The Proof / 14.5:
Counting Simple Graphs / 14.6:
Dirichlet's Pigeonhole Principle / Chapter 15:
The Origin of the Principle / 15.1:
The Pigeonhole Principle / 15.2:
More Applications of the Pigeonhole Principle / 15.3:
Ramsey Theory / Chapter 16:
What is Ramsey's Theorem? / 16.1:
Three Lovely Theorems / 16.2:
Graphs of Many Colors / 16.3:
Euclidean Ramsey Theory / 16.4:
Rook Polynomials and Matchings / Chapter 17:
How Rook Polynomials are Defined / 17.1:
Matchings and Marriages / 17.2:
Solutions to the A Exercises
Books for Further Reading
Index for Notation
Index
Preface to the Second Edition
Acknowledgments
Authors
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