The Maker-Breaker Rado game on a random set of integers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00499813" target="_blank" >RIV/67985840:_____/19:00499813 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/18M117488X" target="_blank" >http://dx.doi.org/10.1137/18M117488X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/18M117488X" target="_blank" >10.1137/18M117488X</a>

Result language
angličtina
Original language name
The Maker-Breaker Rado game on a random set of integers
Original language description
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's 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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