论文标题
$ c-（k，\ ell）$ - 无和套件
$C-(k, \ell)$-Sum-Free Sets
论文作者
论文摘要
Minkowski的两个子集$ a $和$ b $的Minkowski总和定义为$ a $ a $ a $ a和$ b $的所有成对元素：$ a + a + a + b = \ {a + b = \ {a + b：a \ in a，b \ in B \} $中的a \ a \ a \ a \ a \ a \ a \。 $ g $中的$（k，\ ell）$的最大尺寸是$ g $中的无汇总集，在这种情况下，$ g = \ mathbb {z}/n \ mathbb {z} $最近由Bajnok and Matzke计算出来。克拉维兹（Kravitz）由无汇总的圆环集合，引入了两组的嘈杂的Minkowski总和，可以将其视为对这些连续总和的离散评估。也就是说，给定噪声集$ c $，嘈杂的minkowski和定义为$ a + _c b = a + b + c $。在此新总和下，我们给出了$（k，\ ell）$的最大尺寸 - $ \ mathbb {z}/n \ mathbb {z} $的$ \ mathbb {z}/n \ mathbb {z} $的最大范围，对于$ c $，对于等于算术差的$ c $，相当于常见的差异，相对差异为$ n $，对于任何两个元素set $ c $。
The Minkowski sum of two subsets $A$ and $B$ of a finite abelian group $G$ is defined as all pairwise sums of elements of $A$ and $B$: $A + B = \{ a + b : a \in A, b \in B \}$. The largest size of a $(k, \ell)$-sum-free set in $G$ has been of interest for many years and in the case $G = \mathbb{Z}/n\mathbb{Z}$ has recently been computed by Bajnok and Matzke. Motivated by sum-free sets of the torus, Kravitz introduces the noisy Minkowski sum of two sets, which can be thought of as discrete evaluations of these continuous sumsets. That is, given a noise set $C$, the noisy Minkowski sum is defined as $A +_C B = A + B + C$. We give bounds on the maximum size of a $(k, \ell)$-sum-free subset of $\mathbb{Z}/n\mathbb{Z}$ under this new sum, for $C$ equal to an arithmetic progression with common difference relatively prime to $n$ and for any two element set $C$.
