Bijective Combinatorics
Bijective Combinatorics
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双射组合学
DOI：
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发表时间：
2011
期刊：
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通讯作者：
N. Loehr
中科院分区：
文献类型：
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作者：
N. Loehr
在所有数学中，徒证明是一些最优雅，最有力的技术。适用于代数或组合主义者的先前背景的读者，Berixtive Compinatorics提出了枚举和代数组合主义者的一般介绍，强调了生物的方法。该文本在系统上开发了数学工具，例如基本的计数规则，恢复功能，包含 - 分类技术，包含 - 分类技术，求解枚举所需问题。这些工具用于分析许多组合结构，包括单词，排列，子集，功能，组成，整数分区，图形，树木，树木，晶格路径，多层，新鲜分区，固定分区，欧拉尔旅游，eulerian Tours，derangements，posets，posets，abaci，abaci，abaci，abaci of abaci and tillangement，tiiling and abaci of abaci 。这本书还深入研究了组合学的代数方面，提供了正式功率序列，对称组，小组动作，对称多项式，决定因素和tableaux的组合计算的详细处理。每章都包括摘要和广泛的问题集，以审查和加强材料。该文本清醒，引人入胜，但完全严格，描述了许多组合技术，以帮助解决复杂的枚举问题。它涵盖了枚举的基本原则，并应对枚举理论中的族裔证明的作用。
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical tools, such as basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear-algebraic methods, needed to solve enumeration problems. These tools are used to analyze many combinatorial structures, including words, permutations, subsets, functions, compositions, integer partitions, graphs, trees, lattice paths, multisets, rook placements, set partitions, Eulerian tours, derangements, posets, tilings, and abaci. The book also delves into algebraic aspects of combinatorics, offering detailed treatments of formal power series, symmetric groups, group actions, symmetric polynomials, determinants, and the combinatorial calculus of tableaux. Each chapter includes summaries and extensive problem sets that review and reinforce the material. Lucid, engaging, yet fully rigorous, this text describes a host of combinatorial techniques to help solve complicated enumeration problems. It covers the basic principles of enumeration, giving due attention to the role of bijective proofs in enumeration theory.