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- W2791332780 abstract "Given an integer-valued matrix $A$ of dimension $ell times k$ and an integer-valued vector $b$ of dimension $ell$, the Maker-Breaker $(A,b)$-game on a set of integers $X$ is the game where Maker and Breaker take turns claiming previously unclaimed integers from $X$, and Maker's aim is to obtain a solution to the system $Ax=b$, whereas Breaker's aim is to prevent this. When $X$ is a random subset of ${1,dots,n}$ where each number is included with probability $p$ independently of all others, we determine the threshold probability $p_0$ for when the game is Maker or Breaker's win, for a large class of matrices and vectors. This class includes but is not limited to all pairs $(A,b)$ for which $Ax=b$ corresponds to a single linear equation. The Maker's win statement also extends to a much wider class of matrices which include those which satisfy Rado's partition theorem." @default.
- W2791332780 created "2018-03-29" @default.
- W2791332780 creator A5038904202 @default.
- W2791332780 date "2018-03-10" @default.
- W2791332780 modified "2023-09-27" @default.
- W2791332780 title "The Maker-Breaker Rado game on a random set of integers" @default.
- W2791332780 hasPublicationYear "2018" @default.
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