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# Introduction to Combinatorics and Graph Theory

## David Guichard

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### Detalles del libro:

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 Año: 2014 Editor: Autoedición Páginas: 123 páginas Idioma: inglés Desde: 30/01/2015 Tamaño: 869 KB Licencia: Pendiente de revisión

### Contenido:

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).

Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A "graph" in this context is made up of "vertices" or "nodes" and lines called edges that connect them. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.

Contents:

• Fundamentals
• Inclusion-Exclusion
• Generating Functions
• Systems of Distinct Representatives
• Graph Theory
• Polya-Redfield Counting

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