Foundations of Combinatorics with ApplicationsDover Publications, 2006 - 468 strán (strany) This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises. |
Obsah
Notes and References | 39 |
Decision Trees | 67 |
Notes and References | 91 |
Autorské práva | |
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Foundations of Combinatorics with Applications Edward A. Bender,S. Gill Williamson Obmedzený náhľad - 2013 |
Časté výrazy a frázy
automaton Batcher sort bijection binomial coefficients blocks called choose chromatic polynomial coefficients combinatorial compute connected construct contains counting cycle decision tree define definition digit digraph elements equation equivalence relation exactly Example Exercise Figure finite follows formula full binary RP-trees gives graph G Gray code Hint induction input labeled leaf Let G lex order lineal spanning tree look machine merge sort method multiple n-set n-vertex n₁ notation number of comparisons number of edges number of leaves number of vertices obtain ordinary generating function partial fractions partition path permutation polynomial positive integers possible problem proof prove Quicksort random rank recursive algorithm result root Rule of Product Rules of Sum Section sequence simple graph solution sorting network spanning tree step string structures subgraph subsets Suppose T₁ Theorem unlabeled full binary unlabeled RP-trees unranking v₁ values vertex y₁ zeroes