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 Abel Symposium (2016 : Rosendal, Norway)
 Cham, Switzerland : Springer, 2018.
 Description
 Book — 1 online resource (xi, 737 pages) : illustrations (some color).
 Summary

 Facilitated Exclusion Process: Jinho Baik et al
 Stochastic Functional Differential Equations and Sensitivity to their Initial Path: D. R. Baños et al
 Grassmannian Flows and Applications to Nonlinear Partial Differential Equations: Margaret Beck et al
 Gog and Magog Triangles: Philippe Biane
 The Clebsch Representation in Optimal Control and Low Rank Integrable Systems: Anthony M. Bloch et al
 The Geometry of Characters of Hopf Algebras: Geir Bogfjellmo et al
 Shape Analysis on Homogeneous Spaces: a Generalised SRVT Framework: E. Celledoni et al
 Universality in Numerical Computation with Random Data. Case Studies, Analytical Results and Some Speculations: Percy Deift et al
 BSDEs with Default Jump: Roxana Dumitrescu et al
 The Faà di Bruno Hopf Algebra for Multivariable Feedback Recursions in the Center Problem for Higher Order Abel Equations: Kurusch EbrahimiFard et al
 ContinuousTime Autoregressive MovingAverage Processes in Hilbert Space: Fred Espen Benth et al
 Pre and PostLie Algebras: The AlgebroGeometry View: Gunnar Fløystad et al
 Extension of the Product of a PostLie Algebra and Application to the SISO Feedback Transformation Group: Loïc Foissy
 Infinite Dimensional Rough Dynamics: M. Gubinelli
 Heavy Tailed Random Matrices: How They Differ from the GOE, and Open Problems: Alice Guionnet
 An Analyst’s Take on the BPHZ Theorem: Martin Hairer
 Parabolic Anderson Model with Rough Dependence in Space: Yaozhong Hu et al
 Perturbation of Conservation Laws and Averaging on Manifolds: XueMei Li
 Free Probability, Random Matrices, and Representations of NonCommutative Rational Functions: Tobias Mai et al
 A Review on ComoduleBialgebras: Dominique Manchon
 Renormalization: a QuasiShuffle Approach: Frédéric Menous et al
 Hopf Algebra Techniques to Handle Dynamical Systems and Numerical Integrators: A. Murua et al
 Quantitative Limit Theorems for Local Functionals of Arithmetic Random Waves: Giovanni Peccati et al
 Combinatorics on Words and the Theory of Markoff: Christophe Reutenauer
 An Algebraic Approach to Integration of Geometric Rough Paths: Danyu Yang. .
 Hall, M.
 Dordrecht : Springer Netherlands, 1975.
 Description
 Book — 1 online resource (496 pages).
 Summary

 1
 Theory of Designs
 Indeterminates and Incidence Matrices
 Constructions and Uses of Pairwise Balanced Designs
 On Transversal Designs
 Finite Geometry
 Combinatorics of Finite Geometries
 On Finite NonCommutative Affine Spaces
 Coding Theory
 Weight Enumerators of Codes
 The Association Schemes of Coding Theory
 Recent Results on Perfect Codes and Related Topics
 Irreducible Cyclic Codes and Gauss Sums
 2
 Graph Theory
 Isomorphism Problems for Hypergraphs
 Extremal Problems for Hypergraphs
 Applications of Ramsey Style Theorems to Eigenvalues of Graphs
 Foundations, Partitions and Combinatorial Geometry
 Some Recent Developments in Ramsey Theory
 On an Extremal Property of Antichains in Partial orders. The LYM Property and Some of Its Implications and Applications
 Sperner Families and Partitions of a Partially Ordered Set
 Combinatorial Reciprocity Theorems
 3
 Combinatorial Group Theory
 Difference Sets
 Invariant Relations, Coherent Configurations and Generalized Polygons
 2Transitive Designs
 Suborbits in Transitive Permutation Groups
 Groups, Polar Spaces and Related Structures.
 Goldberg, Mark, 1940
 Falls Church, VA (7700 Leesburg Pike, #212, Falls Church 22043) : Delphic Associates, [1983]
 Description
 Book — vii, 97 leaves : ill. ; 28 cm.
 Online
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QA164 .G64 1983  Available 
4. International journal of combinatorics [2009  ]
 [New York, NY] : Hindawi Publishing Corporation
 Description
 Journal/Periodical
 Séminaire lotharingien de combinatoire (Online)
 Séminaire lotharingien de combinatoire.
 Strasbourg : Séminaire lotharingien de combinatoire
 Description
 Journal/Periodical
 Stanley, Richard P., 1944 author.
 Second edition.  Cham, Switzerland : Springer, 2018.
 Description
 Book — 1 online resource (xvi, 263 pages) : illustrations.
7. Combinatorics [2018]
 Bijective combinatorics
 Loehr, Nicholas A., author.
 Second edition.  Boca Raton, FL : CRC Press, Taylor & Francis Group, [2018]
 Description
 Book — xxiv, 618 pages ; 27 cm.
 Summary

 PART 1: ENUMERATION.
 Chapter 1: Basic Counting
 Chapter 2: Combinatorial Identities and Recursions
 Chapter 3: Counting Problems in Graph Theory
 Chapter 4: InclusionExclusion and Related Techniques New
 Chapter 5: Generating Functions
 Chapter 6: Ranking, Unranking, and Successor Algorithms
 PART 2: ALGEBRAIC COMBINATORICS
 Chapter 7: Permutation Statistics and qAnalogues
 Chapter 8: Permutations and Group Actions
 Chapter 9: Tableaux and Symmetric Polynomials.
 Chapter 10: Abaci and Antisymmetric Polynomials
 Chapter 11: Additional Topics. New Appendix: Background in Abstract Algebra.
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QA164 .L64 2018  Unknown 
 Wilson, Robin J., author.
 [Oxford] : Oxford University Press, 2016.
 Description
 Book — 1 online resource : illustrations (black and white).
 Summary

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocketsized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
(source: Nielsen Book Data) 9780198723493 20160704
9. Introduction to combinatorics [2013]
 Erickson, Martin J., 1963
 Second Edition.  Hoboken, New Jersey : John Wiley & Sons, [2013]
 Description
 Book — xii, 230 pages : illustrations ; 25 cm.
 Summary

 Preface xi
 1 Basic Counting Methods
 1 1.1 The multiplication principle
 1 1.2 Permutations
 4 1.3 Combinations
 6 1.4 Binomial coefficient identities
 10 1.5 Distributions
 19 1.6 The principle of inclusion and exclusion
 23 1.7 Fibonacci numbers
 31 1.8 Linear recurrence relations
 33 1.9 Special recurrence relations
 41 1.10 Counting and number theory
 45 Notes
 50
 2 Generating Functions
 53 2.1 Rational generating functions
 53 2.2 Special generating functions
 63 2.3 Partition numbers
 76 2.4 Labeled and unlabeled sets
 80 2.5 Counting with symmetry
 86 2.6 Cycle indexes
 93 2.7 Polya s theorem
 96 2.8 The number of graphs
 98 2.9 Symmetries in domain and range
 102 2.10 Asymmetric graphs
 103 Notes
 105
 3 The Pigeonhole Principle
 107 3.1 Simple examples
 107 3.2 Lattice points, the Gitterpunktproblem, and SET (R)
 110 3.3 Graphs
 115 3.4 Colorings of the plane
 118 3.5 Sequences and partial orders
 119 3.6 Subsets
 124 Notes
 126
 4 Ramsey Theory
 131 4.1 Ramsey s theorem
 131 4.2 Generalizations of Ramsey s theorem
 135 4.3 Ramsey numbers, bounds, and asymptotics
 139 4.4 The probabilistic method
 143 4.5 Sums
 145 4.6 Van der Waerden s theorem
 146 Notes
 150
 5 Codes
 153 5.1 Binary codes
 153 5.2 Perfect codes
 156 5.3 Hamming codes
 158 5.4 The Fano Configuration
 162 Notes
 168
 6 Designs
 171 6.1 tdesigns
 171 CONTENTS ix 6.2 Block designs
 175 6.3 Projective planes
 180 6.4 Latin squares
 182 6.5 MOLS and OODs
 185 6.6 Hadamard matrices
 188 6.7 The Golay code and S(5, 8, 24)
 194 6.8 Lattices and sphere packings
 197 6.9 Leech s lattice
 199 Notes
 201 A Web Resources
 205 B Notation
 207 Exercise Solutions
 211 References
 225 Index 227.
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QA164 .E74 2013  Unknown 
 Goldengorin, Boris.
 New York : Springer, c2012.
 Description
 Book — 1 online resource (x, 114 p.) : ill.
 Summary

 1. Introduction. 2. Maximization of Submodular Functions: Theory and Algorithms. 3. Data Correcting Approach for the Maximization of Submodular Functions. 4. Data Correcting Approach for the Simple Plant Location Problem. References.
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11. Bijective combinatorics [2011]
 Loehr, Nicholas A.
 Boca Raton, FL : Chapman & Hall/CRC, c2011.
 Description
 Book — xxii, 590 p. : ill. ; 27 cm.
 Summary

 Introduction Basic Counting Review of Set Theory Sum Rule Product Rule Words, Permutations, and Subsets Functions Bijections, Cardinality, and Counting Subsets, Binary Words, and Compositions Subsets of a Fixed Size Anagrams Lattice Paths Multisets Probability Games of Chance Conditional Probability and Independence Combinatorial Identities and Recursions Generalized Distributive Law Multinomial and Binomial Theorems Combinatorial Proofs Recursions Recursions for Multisets and Anagrams Recursions for Lattice Paths Catalan Recursions Integer Partitions Set Partitions Surjections Stirling Numbers and Rook Theory Linear Algebra Review Stirling Numbers and Polynomials Combinatorial Proofs of Polynomial Identities Counting Problems in Graph Theory Graphs and Digraphs Walks and Matrices DAG's and Nilpotent Matrices Vertex Degrees Functional Digraphs Cycle Structure of Permutations Counting Rooted Trees Connectedness and Components Forests Trees Counting Trees Pruning Maps Ordered Trees and Terms Ordered Forests and Lists of Terms Graph Coloring Spanning Trees MatrixTree Theorem Eulerian Tours InclusionExclusion and Related Techniques Involutions The InclusionExclusion Formula More Proofs of InclusionExclusion Applications of the InclusionExclusion Formula Derangements Coefficients of Chromatic Polynomials Classical Mobius Inversion Partially Ordered Sets Mobius Inversion for Posets Product Posets Ranking and Unranking Ranking, Unranking, and Related Problems Bijective Sum Rule Bijective Product Rule Ranking Words Ranking Permutations Ranking Subsets Ranking Anagrams Ranking Integer Partitions Ranking Set Partitions Ranking Card Hands Ranking Dyck Paths Ranking Trees Successors and Predecessors Random Selection Counting Weighted Objects Weighted Sets Inversions WeightPreserving Bijections Sum and Product Rules for Weighted Sets Inversions and Quantum Factorials Descents and Major Index Quantum Binomial Coefficients Quantum Multinomial Coefficients Foata's Map Quantum Catalan Numbers Formal Power Series The Ring of Formal Power Series Finite Products and Powers of Formal Series Formal Polynomials Order of Formal Power Series Formal Limits, Infinite Sums, and Infinite Products Multiplicative Inverses in K[x] and K[[x]] Formal Laurent Series Formal Derivatives Composition of Polynomials Composition of Formal Power Series Generalized Binomial Expansion Generalized Powers of Formal Series Partial Fraction Expansions Application to Recursions Formal Exponentiation and Formal Logarithms Multivariable Polynomials and Formal Series The Combinatorics of Formal Power Series Sum Rule for Infinite Weighted Sets Product Rule for Infinite Weighted Sets Generating Functions for Trees Compositional Inversion Formulas Generating Functions for Partitions Partition Bijections Euler's Pentagonal Number Theorem Stirling Numbers of the First Kind Stirling Numbers of the Second Kind The Exponential Formula Permutations and Group Actions Definition and Examples of Groups Basic Properties of Groups Notation for Permutations Inversions and Sign Determinants Multilinearity and Laplace Expansions CauchyBinet Formula Subgroups Automorphism Groups of Graphs Group Homomorphisms Group Actions Permutation Representations Stable Subsets and Orbits Cosets The Size of an Orbit Conjugacy Classes in Sn Applications of the Orbit Size Formula The Number of Orbits Polya's Formula Tableaux and Symmetric Polynomials Partition Diagrams and Skew Shapes Tableaux Schur Polynomials Symmetric Polynomials Homogeneous Symmetric Polynomials Symmetry of Schur Polynomials Orderings on Partitions Schur Bases Tableau Insertion Reverse Insertion Bumping Comparison Theorem Pieri Rules Schur Expansion of halpha Schur Expansion of ealpha Algebraic Independence PowerSum Symmetric Polynomials Relations between e's and h's Generating Functions for e's and h's Relations between p's, e's, and h's PowerSum Expansion of hn and en The Involution omega Permutations and Tableaux Words and Tableaux Matrices and Tableaux Cauchy Identities Dual Bases Abaci and Antisymmetric Polynomials Abaci and Integer Partitions Jacobi Triple Product Identity Ribbons and kCores kQuotients and Hooks Antisymmetric Polynomials Labeled Abaci Pieri Rule for pk Pieri Rule for ek Pieri Rule for hk Antisymmetric Polynomials and Schur Polynomials RimHook Tableaux Abaci and Tableaux Skew Schur Polynomials JacobiTrudi Formulas Inverse Kostka Matrix Schur Expansion of Skew Schur Polynomials Products of Schur Polynomials Additional Topics Cyclic Shifting of Paths ChungFeller Theorem RookEquivalence of Ferrers Boards Parking Functions Parking Functions and Trees Mobius Inversion and Field Theory Quantum Binomial Coefficients and Subspaces Tangent and Secant Numbers Tournaments and the Vandermonde Determinant HookLength Formula Knuth Equivalence Pfaffians and Perfect Matchings Domino Tilings of Rectangles Answers and Hints to Selected Exercises Bibliography Index A Summary and Exercises appear at the end of each chapter.
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QA164 .L64 2011  Available 
 Camina, A. R.
 London ; New York : Springer, c2011.
 Description
 Book — xii, 235 p.
 Online

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13. A combinatorial miscellany [2010]
 Björner, Anders.
 Geneve : L'Enseignement mathematique, 2010.
 Description
 Book — 164 p. : ill. ; 24 cm.
 Online
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QA164 .B567 2010  Unknown 
14. Combinatorics : a guided tour [2010]
 Mazur, David R.
 Washington, DC : Mathematical Association of America, c2010.
 Description
 Book — xviii, 391 p. : ill. ; 27 cm.
 Summary

 Preface Before you go Notation Part I. Principles of Combinatorics:
 1. Typical counting questions, the product principle
 2. Counting, overcounting, the sum principle
 3. Functions and the bijection principle
 4. Relations and the equivalence principle
 5. Existence and the pigeonhole principle Part II. Distributions and Combinatorial Proofs:
 6. Counting functions
 7. Counting subsets and multisets
 8. Counting set partitions
 9. Counting integer partitions Part III. Algebraic Tools:
 10. Inclusionexclusion
 11. Mathematical induction
 12. Using generating functions, part I
 13. Using generating functions, part II
 14. techniques for solving recurrence relations
 15. Solving linear recurrence relations Part IV. Famous Number Families:
 16. Binomial and multinomial coefficients
 17. Fibonacci and Lucas numbers
 18. Stirling numbers
 19. Integer partition numbers Part V. Counting Under Equivalence:
 20. Two examples
 21. Permutation groups
 22. Orbits and fixed point sets
 23. Using the CFB theorem
 24. Proving the CFB theorem
 25. The cycle index and Polya's theorem Part VI. Combinatorics on Graphs:
 26. Basic graph theory
 27. Counting trees
 28. Colouring and the chromatic polynomial
 29. Ramsey theory Part VII. Designs and Codes:
 30. Construction methods for designs
 31. The incidence matrix, symmetric designs
 32. Fisher's inequality, Steiner systems
 33. Perfect binary codes
 34. Codes from designs, designs from codes Part VIII. Partially Ordered Sets:
 35. Poset examples and vocabulary
 36. Isomorphism and Sperner's theorem
 37. Dilworth's theorem
 38. Dimension
 39. Moebius inversion, part I
 40. Moebius inversion, part II Bibliography Hints and answers to selected exercises.
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QA164 .M398 2010  Unknown 
 Pólya, George, 18871985.
 Boston : Birkhäuser, c2010.
 Description
 Book — 190, [1] p. : ill.
 Summary

 Introduction. Combinations and Permutations. Generating Functions. Principle of Inclusion and Exclusion. Stirling Numbers. Polya's Theory of Counting. Outlook. Midterm Examination. Ramsey Theory. Matchings (Stable Marriages). Matchings (Maximum Matchings). Network Flow. Hamiltonian and Eulerian Paths. Planarity and the FourColor Theorem. Final Examination. Bibliography.
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16. Analytic combinatorics [2009]
 Flajolet, Philippe.
 Cambridge, UK ; New York : Cambridge University Press, 2009.
 Description
 Book — xiii, 810 p. : ill. ; 26 cm.
 Summary

 Preface An invitation to analytic combinatorics Part A. Symbolic Methods:
 1. Combinatorial structures and ordinary generating functions
 2. Labelled structures and exponential generating functions
 3. Combinatorial parameters and multivariate generating functions Part B. Complex Asymptotics:
 4. Complex analysis, rational and meromorphic asymptotics
 5. Applications of rational and meromorphic asymptotics
 6. Singularity analysis of generating functions
 7. Applications of singularity analysis
 8. SaddlePoint asymptotics Part C. Random Structures:
 9. Multivariate asymptotics and limit laws Part D. Appendices: Appendix A. Auxiliary elementary notions Appendix B. Basic complex analysis Appendix C. Concepts of probability theory Bibliography Index.
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QA164 .F553 2009  Unavailable Out for repair Request 
17. Applied combinatorics [2009]
 Roberts, Fred S.
 2nd ed.  Boca Raton, Fla. : CRC Press/Taylor & Francis Group, c2009.
 Description
 Book — xxvii, 860 p. : ill. ; 27 cm.
 Summary

 What Is Combinatorics? THE BASIC TOOLS OF COMBINATORICS: Basic Counting Rules. Introduction to Graph Theory. Relations. THE COUNTING PROBLEM: Generating Functions and Their Applications. Recurrence Relations. The Principle of Inclusion and Exclusion. The Polya Theory of Counting. THE EXISTENCE PROBLEM: Combinatorial Designs. Coding Theory. Existence Problems in Graph Theory. COMBINATORIAL OPTIMIZATION: Matching and Covering. Optimization Problems for Graphs and Networks. Appendix. Indices.
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QA164 .R6 2009  Unknown 
18. Lectures on advances in combinatorics [2008]
 Ahlswede, Rudolf, 1938
 Berlin : Springer, c2008.
 Description
 Book — xiii, 314 p. : ill. ; 24 cm.
 Summary

 Conventions and Auxiliary Results. Intersection and Diametric Problems. Covering, Packing and List Codes. Higher Level and Dimension Constrained Extremal Problems. LYMrelated AZIdentities, Antichain Splittings and Correlation Inequalities. Basic Problems from Combinatorial Number Theory. Appendix: Supplementary Matrial and Research Problems. References. Index.
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QA164 .A35 2008  Available 
 Ahlswede, Rudolf, 1938
 Berlin : Springer, 2008.
 Description
 Book — xiii, 314 p. : ill.
20. Additive combinatorics [2006]
 Tao, Terence, 1975
 Cambridge ; New York : Cambridge University Press, 2006.
 Description
 Book — xviii, 512 p. ; 24 cm.
 Summary

 Prologue
 1. The probabilistic method
 2. Sum set estimates
 3. Additive geometry
 4. Fourieranalytic methods
 5. Inverse sum set theorems
 6. Graphtheoretic methods
 7. The LittlewoodOfford problem
 8. Incidence geometry
 9. Algebraic methods
 10. Szemeredi's theorem for k = 3
 11. Szemeredi's theorem for k > 3
 12. Long arithmetic progressions in sum sets Bibliography Index.
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QA164 .T36 2006  Unknown 
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