论文标题
薄弱的Schur分区的新下限
New lower bounds for weak Schur partitions
论文作者
论文摘要
本文记录了一些明显的新结果，该结果将整数间隔[1，n]分配到弱的无量子集中。这些是使用与Schur在1917年使用的方法密切相关的方法生产的。可以以这种方式生成新的下限，以用于无限尺寸的分区。随着子集的数量的增加，下限的渐近生长速率不能小于相同的无和分区的增长率，因此超过3.27。分区中的分区的具体结果包括$ WS（6）\ GE 642 $，$ WS（7）\ GE 2146 $，$ WS（8）\ GE 6976 $，$ WS（9）\ GE 21848 $和$ WS（10）\ GE 707778 $。
This paper records some apparently new results for the partition of integer intervals [1, n] into weakly sum-free subsets. These were produced using a method closely related to that used by Schur in 1917. New lower bounds can be produced in this way for partitions of unlimited size. The asymptotic growth rate of the lower bounds, as the number of subsets increases, cannot be less than the same growth rate for strongly sum-free partitions, and therefore exceeds 3.27. Specific results for partitions into a 'small' number of subsets include $WS(6) \ge 642$, $WS(7) \ge 2146$, $WS(8) \ge 6976$, $WS(9) \ge 21848$, and $WS(10) \ge 70778$.
