Posts / combinatorics

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This is my semi active blog, each article is a by-product of me attempting to understand some mathematics. Most articles, hence, are just rehashes of existing literature and most original contributions are either through mistakes which I apologise for in advance, or through non-traditional reordering of topics to suit my taste. It can however provide a starting point to some of the content, or an alternate perspective if you're already familiar with the material.

Winning Strategies

August 6, 2020 (combinatorics)

The summer of 2020 found me working on set theoretic questions with Dr Thomas Forster– one of the first tasks he set me was to read about Conway’s Sylver Coinage. This simple question opens up a discussion of the theory of Gale-Stewart games, where two players take turns to build infinite sequences of natural numbers. The winner is decided based on whether or not the resulting sequence has some property– and knowing things as simple as the cardinality of all winning configurations can reveal a lot about whether the game has a winning strategy, i.e. is rigged in favour of one of the players.