Aspects of combinatorics and combinatorial number theory

By:

Adhikari, Sukumar Das

Material type: Text

TextPublication details: Pangbourne, England : Alpha Science International, cop. 2002.Description: xiv, 156 pages : illustrationsISBN:

9781842650493
1842650491

Subject(s):

Ramsey theory

DDC classification:

511.6 ADH

Contents:

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.

Summary: 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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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Reference Books	Main Library Reference	Reference	511.6 ADH (Browse shelf(Opens below))	Available		009577

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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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