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13 of 17 people found the following review helpful:
5.0 out of 5 stars
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This review is from: Constructive Combinatorics (Undergraduate Texts in Mathematics) (Paperback)
Unlike other textbook in the prosperous combinatorics , this introduction book takes a very different pace.It's paradigm is "SHOW me the proof". From the very beginning to the last page ,authors us that we can make a proof clear by write out directly the algorithm or just make a apparent bijection. The book contains 4 chapters, the first 2 stress on basic enumeration objects and posets, the last 2 on bijection and involution. With authour's carefully-selected topic and examples, this book is self-contained. this book shows us the splendid new concepts of combinatorics. I must say that I'm very happy and shocked that ,in such a few pages ,by using combinatorical method developed here we can EASILY prove Cayley's theorem, Vandemonde determinent, Roger-Ramanujan's partition formula. etc. The exercises are excellent too. Very many good seed ideas waiting to be developed.
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Inside This Book
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First Sentence:
At a basic level, one would expect that constructive combinatorics would address the question of how one constructs the fundamental objects in combinatorics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rank unimodal, column insertion algorithm, colex order, lex list, symmetric chain decomposition, column strict tableaux, involution principle, multiset permutations, restricted growth function, whose largest part, pentagonal number theorem, listing algorithms, lattice paths, hook formula, standard tableaux, ballot problem, bijective proof, terminal vertices, combinatorial proof, integer partitions, signed set, inversion sequence, rank symmetric, increasing subsequence, full binary tree Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Kruskal-Katona Theorem, Cayley-Hamilton Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
At a basic level, one would expect that constructive combinatorics would address the question of how one constructs the fundamental objects in combinatorics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rank unimodal, column insertion algorithm, colex order, lex list, symmetric chain decomposition, column strict tableaux, involution principle, multiset permutations, restricted growth function, whose largest part, pentagonal number theorem, listing algorithms, lattice paths, hook formula, standard tableaux, ballot problem, bijective proof, terminal vertices, combinatorial proof, integer partitions, signed set, inversion sequence, rank symmetric, increasing subsequence, full binary tree Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Kruskal-Katona Theorem, Cayley-Hamilton Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 48
books:
See all 48 books this book cites
100
books
cite this book:
See all 100 books citing this book
- Introduction to Combinatorial Mathematics (Computer Science Series) by Chung L. Liu in Back Matter
- Applied Combinatorics by Alan Tucker in Back Matter
- Linear Algebra (Oxford Science Publications) by Richard Kaye in Back Matter
- A Brief on Tensor Analysis (Undergraduate Texts in Mathematics) by James G. Simmonds in Back Matter
- General Topology (Undergraduate Texts in Mathematics) by J. Dixmier in Front Matter
See all 48 books this book cites
- Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions) by Arthur T. Benjamin in Front Matter, page 89, and Back Matter
- Enumerative Combinatorics, Volume 2 by Richard P. Stanley on page 412, and page 498
- Symbolic Computation in Undergraduate Mathematics Education (M a a Notes) by Zaven A. Karian on page 5 (1), and page 5 (2)
- Factorization and Primality Testing (Undergraduate Texts in Mathematics) by David M. Bressoud in Front Matter, and Back Matter
- Basic Topology (Undergraduate Texts in Mathematics) by M.A. Armstrong in Back Matter (1), and Back Matter (2)
See all 100 books citing this book
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