Invariants

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

Chapter 3 in Problem-Solving Methods in Combinatorics, 2013, pp 27-41 from Springer

Abstract: Abstract This chapter shows how invariants can be used in combinatorial problems. First, we show some examples that go from purely combinatorial problems to geometric ones, and how invariants are used to solve each of them. Then, we present in depth how coloring techniques are used in problems related to boards, especially those concerning some type of tiling. Then, we introduce some concepts related to game theory, and show how some problems of this kind can be solved using invariants. At the end of the chapter, 23 problems are given for the reader to practice.

Keywords: Geometric Ones; Chessboard Coloring; Combinatorial Geometry Problems; International Mathematical Olympiad; Knight Attacks (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-0348-0597-1_3

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