# Aspects of combinatorics and combinatorial number theory

Material type: TextPublication details: Pangbourne, England : Alpha Science International, cop. 2002Description: xiv, 156 pages : illustrationsISBN: 9781842650493 ; 1842650491 Subject(s): Ramsey theoryDDC classification: 511.6Item type | Current library | Collection | Call number | Status | Date due | Barcode | Item holds |
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Reference Books | Main Library Reference | Reference | 511.6 ADH (Browse shelf(Opens below)) | Available | 009577 |

Ch. 1. Classical Ramsey-type theorems. The Pigeonhole Principle. Theorems of Ramsey and Erdos-Szekeres. van der Waerden's Theorem. Schur's Theorem. A theorem of Hilbert --

Ch. 2. van der Waerden revisited. Hales-Jewett theorem. Some variations of van der Waerden's theorem --

Ch. 3. Generalizations of Schur's theorem. Rado's theorem. Folkman's theorem --

Ch. 4. Topological methods. Compact semigroups and idempotents. Ramsey-type theorems --

Ch. 5. Euclidean Ramsey theory. Preliminaries. Fundamental Theorems. Further Ramsey configurations. A theorem of Graham --

Ch. 6. Additive number Theory and related questions. Zero-sum problems. A question of Sidon and some related problems --

Ch. 7. Partitions of integers. Preliminaries. Generating functions. An identity of Euler. Parity of partition function --

Ch. 8. Ramsey-type results in posets. Preliminaries. A theorem of Harzheim. Generalizations --

Ch. 9. Solutions to selected exercises.

The author begins with a discussion of various Ramsey-type theorems in combinatorics and combinatorial number theory. He then moves on to describe many recent Ramsey-type results in combinatorics with application of topological ideas

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