A walk through combinatorics : an introduction to enumeration and graph theory /
The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially o...
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| Format: | Book |
| Language: | English |
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Hackensack, NJ :
World Scientific Pub.,
[2006], ©2006
Hackensack, NJ : c2006 New Jersey : c2006 |
| Edition: | 2nd ed |
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| 100 | 1 | |a Bóna, Miklós |0 http://viaf.org/viaf/69152671 | |
| 100 | 1 | |a Bóna, Miklós |1 http://viaf.org/viaf/69152671 | |
| 100 | 1 | |a Bóna, Miklós | |
| 100 | 1 | |a Bóna, Miklós | |
| 245 | 1 | 2 | |a A walk through combinatorics : |b an introduction to enumeration and graph theory / |c Miklós Bóna |
| 250 | |a 2nd ed | ||
| 260 | |a Hackensack, NJ : |b World Scientific Pub., |c [2006], ©2006 | ||
| 260 | |a Hackensack, NJ : |b World Scientific Pub., |c c2006 | ||
| 260 | |a New Jersey : |b World Scientific Pub., |c c2006 | ||
| 300 | |a xvii, 469 p. : |b ill. ; |c 24 cm | ||
| 300 | |a xvii, 469 pages : |b illustrations ; |c 24 cm | ||
| 300 | |a xviii, 469 p. : |b ill. ; |c 24 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 500 | |a This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC |5 CTY | ||
| 504 | |a Includes bibliographical references (p. 461-463) and index | ||
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | |a pt. 1. Basic methods -- Seven is more than six. The pigeon-hole principle -- One step at a time. The method of mathematical induction -- pt. 2. 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 -- pt. 3. 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 -- pt. 4. 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 | |
| 505 | 0 | 0 | |g 1 |t Seven is more than six : the pigeon-hole principle -- |g 2. |t One step at a time : the method of mathematical induction -- |g 3. |t There are a lot of them : elementary counting problems -- |g 4. |t No matter how you slice it : the binomial theorem and related identities -- |g 5. |t Divide and conquer : partitions -- |g 6. |t Not so vicious cycles : cycles in permutations -- |g 7. |t You shall not overcount : the sieve -- |g 8. |t A function is worth many numbers : generating functions -- |g 9. |t Dots and lines : the origins of graph theory -- |g 10. |t Staying connected : trees -- |g 11. |t Finding a good match : coloring and matching -- |g 12. |t Do not cross : planar graphs -- |g 13. |t Does it clique? : Ramsey theory -- |g 14. |t So hard to avoid : subsequence conditions on permutations -- |g 15. |t Who knows what it looks like, but it exists : the probabilistic method -- |g 16. |t At least some order : partial orders and lattices -- |g 17. |t The sooner the better : combinatorial algorithms -- |g 18. |t Does many mean more than one? : computational complexity. |
| 505 | 0 | 0 | |g 1 |t Seven is more than six : the pigeon-hole principle -- |g 2. |t One step at a time : the method of mathematical induction -- |g 3. |t There are a lot of them : elementary counting problems -- |g 4. |t No matter how you slice it : the binomial theorem and related identities -- |g 5. |t Divide and conquer : partitions -- |g 6. |t Not so vicious cycles : cycles in permutations -- |g 7. |t You shall not overcount : the sieve -- |g 8. |t A function is worth many numbers : generating functions -- |g 9. |t Dots and lines : the origins of graph theory -- |g 10. |t Staying connected : trees -- |g 11. |t Finding a good match : coloring and matching -- |g 12. |t Do not cross : planar graphs -- |g 13. |t Does it clique? : Ramsey theory -- |g 14. |t So hard to avoid : subsequence conditions on permutations -- |g 15. |t Who knows what it looks like, but it exists : the probabilistic method -- |g 16. |t At least some order : partial orders and lattices -- |g 17. |t The sooner the better : combinatorial algorithms -- |g 18. |t Does many mean more than one? : computational complexity. |
| 520 | |a The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity | ||
| 650 | 0 | |a Combinatorial analysis | |
| 650 | 4 | |a Análisis combinatorio | |
| 650 | 7 | |a Combinatorial analysis |2 fast | |
| 650 | 7 | |a Combinatória |2 larpcal | |
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| 655 | 7 | |a Einführung |2 gnd | |
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