模素幂的组合零元数与奇偶论证
Combinatorial Nullstellensatz modulo prime powers and the Parity Argument
摘要：
我们提出了新的推广奥尔森定理和阿隆的组合零点的后果。这些使我们能够扩展他们的一些组合应用的条件模素数的条件模素数的权力。我们分析了这类组合问题对应的计算搜索问题，证明了寻找度约束子图模$2^d$（如$2^d$ -可除子图）的问题和搜索$\mathbb{F}_2$上的组合零点问题属于复杂性类多项式奇偶论证（PPA）.
英文摘要：
We present new generalizations of Olson's theorem and of a consequence of Alon's Combinatorial Nullstellensatz. These enable us to extend some of their combinatorial applications with conditions modulo primes to conditions modulo prime powers. We analyze computational search problems corresponding to these kinds of combinatorial questions and we prove that the problem of finding degree-constrained subgraphs modulo $2^d$ such as $2^d$-divisible subgraphs and the search problem corresponding to the Combinatorial Nullstellensatz over $\mathbb{F}_2$ belong to the complexity class Polynomial Parity Argument (PPA).
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