A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory
A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory
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DOI：
10.1142/10258
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发表时间：
2006-10
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基本方法：七比六大。鸽子洞原则：一步一步来。数学归纳法、枚举组合法：有很多。基本的计数问题，不管你怎么切它。二项式定理及相关恒等式分治。分区不是恶性循环。排列中的循环你不应该重复计数。筛A函数值很多数。生成函数图论：点与线。图论的起源保持联系。树找到一个好的匹配。上色与配色不交叉。平面图形视界：它会拉帮结派吗？拉姆齐理论如此难以避免。排列的子序列条件谁知道它长什么样，但它确实存在。概率方法至少有一个阶。偏序和格越快越好。组合算法多意味着多于一个吗？计算的复杂性。
Basic Methods: Seven Is More Than Six. The Pigeon-Hole Principle One Step at a Time. The Method of Mathematical Induction Enumerative Combinatorics: There Are a Lot of Them. Elementary Counting Problems No Matter How You Slice It. The Binomial Theorem and Related Identities Divide and Conquer. Partitions Not So Vicious Cycles. Cycles in Permutations You Shall Not Overcount. The Sieve A Function is Worth Many Numbers. Generating Functions Graph Theory: Dots and Lines. The Origins of Graph Theory Staying Connected. Trees Finding a Good Match. Coloring and Matching Do Not Cross. Planar Graphs Horizons: Does It Clique? Ramsey Theory So Hard to Avoid. Subsequence Conditions on Permutations Who Knows What It Looks Like, but It Exists. The Probabilistic Method At Least Some Order. Partial Orders and Lattices The Sooner The Better. Combinatorial Algorithms Does Many Mean More Than One? Computational Complexity.