## Combinatorics for Computer ScienceUseful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures. |

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### Contents

BASIC CONCEPTS OF LINEAR ORDER | 3 |

TOPIC I SORTING | 47 |

BASIC COMBINATORIAL LISTS | 76 |

4 | 98 |

SYMMETRYORBIT ENUMERATION | 114 |

A TRIANGLE | 120 |

We explore some less obvious variations on Burnsides lemma 4 224 | 128 |

SOME CLASSICAL COMBINATORICS | 165 |

5B THE PRINCIPLE OF INCLUSIONEXCLUSION | 182 |

5C MOBIUS INVERSION | 188 |

FLOW THROUGH A NETWORK | 201 |

8 | 263 |

DEPTH FIRST SEARCH | 319 |

TRICONNECTIVITY | 337 |

MATROIDS | 359 |

References for Graphs Trees and Recursion | 450 |

2 integral partitions with no repeated parts and | 171 |

NotAtion FOR THE MULTINOMIAL COEFFICIENT | 173 |

COROLLARY uniqueness of normalized basis sequence | 179 |

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### Common terms and phrases

algebra backedges basic biconnected graph bijection bipartite graph blocks bridge Burnside's lemma called Chapter CNL-tree CNL(M coefficients colex order columns Combinatorial components compute connected consider construct COROLLARY corresponding CYCLE(e data structures define DEFINITION diagram directed graph discussion disjoint edges of G elements embedding entries equivalence equivalence relation example EXERCISE finite given graph G graph theory idea identity incidence algebra independent sets induced matroid integers inverse labeled LEMMA Let G lex order lineal spanning tree linear order linearly Math Möbius Möbius function notation Note obtained orbit order isomorphism ordered partition orderly algorithm path PATH(e PATR(G,T permutation planar Pólya polynomial poset preorder problem procedure proof rank reader recursion representable matroid representatives RG functions row canonical form SEGLST(e segment separation pair sequence shown in FIGURE spanning tree subgraph subset subtree symbols TAIL(F THEOREM Tutte polynomial unit row canonical vector vertex vertices wreath product