In 1991, Craig Gotsman and Nathan Linial conjectured that for all $n$ and $d$, the average sensitivity of a degree-$d$ polynomial threshold function on $n$ variables is maximized by the degree-$d$ symmetric polynomial which computes the parity function on the $d$ layers of the hypercube with Hamming weight closest to $n/2$. We refute the conjecture for almost all $d$ and for almost all $n$, and we confirm the conjecture in many of the remaining cases.
翻译：1991年,克雷格·戈特斯曼和内森·林尼亚尔(Nathan Linial)推测,对于所有美元和美元,以美元变量计算的一度-美元多元阈值的平均灵敏度,由以美元对称多元数值乘以美元乘以1美元乘以1美元乘以1美元乘以2美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1乘以1美元乘以1美元乘以1美元乘以1美元乘以1乘以1美元乘以2美元乘以1乘以1美元乘以1美元乘以1美元乘以1乘以1乘以1乘以1乘以1美元乘以1乘以1乘以1乘以2美元乘以1乘以1美元乘以1乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元计算。 我们驳斥几乎所有美元和1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1美元乘以1乘以1乘以1乘以1乘以1乘以1美元乘以1乘以1乘乘以1乘以1乘以1乘以1乘以1乘以1乘以1乘以1乘乘以计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算的乘1乘1乘1乘1乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘等于计算计算计算计算的乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘乘等于计算计算计算计算计算计算的乘乘乘乘乘等于计算计算计算计算计算计算计算计算计算计算计算计算计算计算计算的乘乘乘乘乘乘乘乘
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