论文标题
从整数到锤子指标
Quasihomomorphisms from the integers into Hamming metrics
论文作者
论文摘要
如果$ f（x+y）$和$ f（x+y）$和$ f（x）+f（y）$之间的hamming距离最多是$ x $ c $，a函数$ f：\ mathbb {z} \ to \ mathbb {q}^n $是$ c $ - quasihomomorphism，则最多最多是$ f（x+y）$和$ f（x）+f（y）$的$ c $ c $ cu $ in \ in \ in \ in \ in \ in \ in \ in \ mathbb {z} $。我们表明，任何$ c $ - quasihomormormormormormormorming to to to to to to co $ c $ quasiihomormormormormorm toss to to to to to to co $ c $ co（c）$与实际的组同构合法性最多有一些恒定的$ c（c）$；这里$ c（c）$仅取决于$ c $，而不取决于$ n $或$ f $。这给了Kazhdan和Ziegler提出的问题的特殊情况。
A function $f: \mathbb{Z} \to \mathbb{Q}^n$ is a $c$-quasihomomorphism if the Hamming distance between $f(x+y)$ and $f(x)+f(y)$ is at most $c$ for all $x,y \in \mathbb{Z}$. We show that any $c$-quasihomomorphism has distance at most some constant $C(c)$ to an actual group homomorphism; here $C(c)$ depends only on $c$ and not on $n$ or $f$. This gives a positive answer to a special case of a question posed by Kazhdan and Ziegler.
