Bijective combinatorics /
Loehr, Nicholas A.
Bijective combinatorics / Nicholas A. Loehr. - Boca Raton, Fla. ; London : CRC Press, c2011. - xxii, 590 p. : ill. ; 27 cm. - Discrete mathematics and its applications. . - Discrete mathematics and its applications. .
"A Chapman & Hall book" --t.p.
Includes bibliographical references and index.
"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" --Provided by publisher.
9781439848845 (hbk. : alk. paper) 143984884X (hbk. : alk. paper)
2011007250
GBB0B4290 bnb
015654735 Uk
Combinatorial analysis.
QA164 / .L64 2011
511/.62
Bijective combinatorics / Nicholas A. Loehr. - Boca Raton, Fla. ; London : CRC Press, c2011. - xxii, 590 p. : ill. ; 27 cm. - Discrete mathematics and its applications. . - Discrete mathematics and its applications. .
"A Chapman & Hall book" --t.p.
Includes bibliographical references and index.
"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" --Provided by publisher.
9781439848845 (hbk. : alk. paper) 143984884X (hbk. : alk. paper)
2011007250
GBB0B4290 bnb
015654735 Uk
Combinatorial analysis.
QA164 / .L64 2011
511/.62