Combinatorics is often described brie y as being about counting, and indeed counting is a large part of combinatorics. As the name suggests, however, it is broader than this: it is about combining things. …

1 Introduction Combinatorics is centered around the most fundamental concept of mathemat-ics: counting. This paper will explore basic enumerative combinatorics, includ-ing permutations, strings, …

2.4 Ramsey Theory at are part of a very important area in Combinatorics known as Ramsey theor them who are mutually friends or three of them who are unknown to each other. We would like to consider …

Preface Enumerative combinatorics has seen an explosive growth over the last 50 years. The purpose of this text is to give a gentle introduction to this exciting area of research. So, rather than trying to …

These notes accompanied the course MAS219, Combinatorics, at Queen Mary, University of London, in the Autumn semester 2007. It is impossible to define combinatorics, but an approximate description …

Combinatorics is a very broad subject. This book gives a straightforward and motivated introduction to four related areas of combinatorics. Each is the subject of current research, and taken together, they …

Combinatorics Based on a handout by Mehran Sahami As we mentioned last class, the principles of counting are core to probability. Counting is like the foundation of a house (where the house is all the …