The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labeled and unlabeled structures as well as a tool for the specification and analysis of these structures. This key reference presents the basic elements of the theory and gives a unified account of its developments and applications. The authors offer a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya Theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis, and differential equations.
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"This is an excellent account of the theory of species, and should make this powerful approach to an important area of combinatorics much more accessible." Mathematical Reviews
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Text: English (translation)
Original Language: French
Original Language: French
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First Sentence:
This chapter contains the basic concepts of the combinatorial theory of species of structures. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dissymmetry theorem, enriched rooted trees, weighted species, virtual species, binomial type sequence, combinatorial equality, plethystic substitution, partial endofunction, functorial composition, partitional composition, plane rooted trees, species theorem, unlabeled rooted trees, combinatorial equalities, ordinary generating series, quotient species, species isomorphism, nonseparable graphs, empty species, exponential generating series, combinatorial equation, binary rooted trees, cycle index polynomial, ordered rooted trees, irreducible trees Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Adapt Algorithm, Pólya-Redfield's Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter contains the basic concepts of the combinatorial theory of species of structures. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dissymmetry theorem, enriched rooted trees, weighted species, virtual species, binomial type sequence, combinatorial equality, plethystic substitution, partial endofunction, functorial composition, partitional composition, plane rooted trees, species theorem, unlabeled rooted trees, combinatorial equalities, ordinary generating series, quotient species, species isomorphism, nonseparable graphs, empty species, exponential generating series, combinatorial equation, binary rooted trees, cycle index polynomial, ordered rooted trees, irreducible trees Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Adapt Algorithm, Pólya-Redfield's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 69
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21
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- Iterative Functional Equations (Encyclopedia of Mathematics and its Applications) by Marek Kuczma in Front Matter, and Back Matter
- Discrete Mathematics: for New Technology by Rowan Garnier in Back Matter (1), and Back Matter (2)
- The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Second Edition (Graduate Texts in Mathematics) by Bruce E. Sagan in Back Matter (1), and Back Matter (2)
- Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi in Front Matter
- Stopping Times and Directed Processes (Encyclopedia of Mathematics and its Applications) by G. A. Edgar in Front Matter
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- Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications) by George Gasper in Front Matter
- Abstract Regular Polytopes (Encyclopedia of Mathematics and its Applications) by Peter McMullen in Front Matter
- Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications) by Alexei Kushner in Front Matter
- Navier-Stokes Equations and Turbulence (Encyclopedia of Mathematics and its Applications) by C. Foias in Front Matter
- The Mountain Pass Theorem: Variants, Generalizations and Some Applications (Encyclopedia of Mathematics and its Applications) by Youssef Jabri in Front Matter
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