Aspects of combinatorics and combinatorial number theory
Adhikari, Sukumar Das
Aspects of combinatorics and combinatorial number theory - Pangbourne, England : Alpha Science International, cop. 2002. - xiv, 156 pages : illustrations ;
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
9781842650493 1842650491
Ramsey theory.
511.6 / ADH
Aspects of combinatorics and combinatorial number theory - Pangbourne, England : Alpha Science International, cop. 2002. - xiv, 156 pages : illustrations ;
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
9781842650493 1842650491
Ramsey theory.
511.6 / ADH