Abstract
This chapter deals with the basic results needed to solve combinatorics problems. We start with set-theoretic definitions and constructions, and then carry on with the most important results needed to start working in combinatorics. Then, stronger solving-problems methods are presented, such as induction, the principle of inclusion-exclusion and the use of delimiters. Throughout the whole chapter there are examples of problems solved with the methods at hand. Even though this is an introductory chapter, we show how using only these methods we are able to solve problems that appeared in international mathematical competitions. At the end of the chapter, a list of 14 problems is given where the reader may practice.
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Notes
- 1.
If you want an example of this, consider Russell’s paradox. Let S be the collection of all sets that do not contain themselves as elements, i.e., all sets A such that A∉A. If S is considered as a set, then S∈S if and only if S∉S, a contradiction!
- 2.
⌊x⌋ denotes the greatest integer that is smaller than or equal to x.
- 3.
The exact value of this number is \(\frac {1}{e}\), where e is the famous Euler constant.
- 4.
In chess, a rook attacks all the pieces in its row and in its column.
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Soberón, P. (2013). First Concepts. In: Problem-Solving Methods in Combinatorics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0597-1_1
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DOI: https://doi.org/10.1007/978-3-0348-0597-1_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0596-4
Online ISBN: 978-3-0348-0597-1
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