关于系数选择博弈

Q4 Mathematics

Moscow Journal of Combinatorics and Number Theory Pub Date : 2020-07-01 DOI:10.2140/moscow.2021.10.183

Divyum Sharma, L. Singhal

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引用次数: 1

摘要

Nora和Wanda是从某个固定酉交换环$R$中选择次$d$多项式系数的两个参与者。如果多项式在$R$的分数环中有根，则Wanda被宣布为获胜者，否则Nora被宣布为胜利者。我们将Gasarch、Washington和Zbarsky给出的这些对策的理论推广到所有有限循环环，并确定了可能的结果。对于这些作者提出的游戏变体，还使用离散估值环构建了一系列例子。

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On the coefficient-choosing game

Nora and Wanda are two players who choose coefficients of a degree $d$ polynomial from some fixed unital commutative ring $R$. Wanda is declared the winner if the polynomial has a root in the ring of fractions of $R$ and Nora is declared the winner otherwise. We extend the theory of these games given by Gasarch, Washington and Zbarsky to all finite cyclic rings and determine the possible outcomes. A family of examples is also constructed using discrete valuation rings for a variant of the game proposed by these authors.

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来源期刊

Moscow Journal of Combinatorics and Number Theory Mathematics-Algebra and Number Theory

CiteScore

0.80

自引率

0.00%

发文量