Functions

Pablo Soberón
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Pablo Soberón: University College London, Department of Mathematics

Chapter 5 in Problem-Solving Methods in Combinatorics, 2013, pp 59-76 from Springer

Abstract: Abstract This chapter presents how to use functions in combinatorial problems. The main objective is that the reader sees how constructing functions and observe basic properties of them can help to deduce meaningful information about the problem. This is done in the first section. Then, we study permutations. We analyze their structure and some of their properties that make working with them easier. Once this machinery is set up, we show examples where this can be helpful. In the next section, we introduce the concept of counting twice. This technique has been used throughout the book, but now we view this properly from a functional point of view, with examples from math olympiads of increasing difficulty. Finally, we show a simple proof of the Erdős-Ko-Rado theorem with a double counting argument. This shows the power that this innocent-looking technique has. At the end of the chapter, 19 problems are presented.

Keywords: Double Counting Argument; Permutation; Single Lamp; Bijective Mapping; Cycle Decomposition (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0597-1_5

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DOI: 10.1007/978-3-0348-0597-1_5

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