We present a revisit of the seeds algorithm to explore the semigroup tree. First, an equivalent definition of seed is presented, which seems easier to manage. Second, we determine the seeds of semigroups with at most three left elements. And third, we find the great-grandchildren of any numerical semigroup in terms of its seeds. The RGD algorithm is the fastest known algorithm at the moment. But if one compares the originary seeds algorithm with the RGD algorithm, one observes that the seeds algorithm uses more elaborated mathematical tools while the RGD algorithm uses data structures that are better adapted to the final C implementations. For genera up to around one half of the maximum size of native integers, the newly defined seeds algorithm performs significantly better than the RGD algorithm. For future compilators allowing larger native sized integers this may constitute a powerful tool to explore the semigroup tree up to genera never explored before. The new seeds algorithm uses bitwise integer operations, the knowledge of the seeds of semigroups with at most three left elements and of the great-grandchildren of any numerical semigroup, apart from techniques such as parallelization and depth first search as wisely introduced in this context by Fromentin and Hivert. The algorithm has been used to prove that there are no Eliahou semigroups of genus $66$, hence proving the Wilf conjecture for genus up to $66$. We also found three Eliahou semigroups of genus $67$. One of these semigroups is neither of Eliahou-Fromentin type, nor of Delgado's type. However, it is a member of a new family suggested by Shalom Eliahou.

翻译：本文重新审视了种子算法以探索半群树。首先，提出了一种等价定义，似乎更易于处理。其次，确定了最多包含三个左侧元素的半群的种子。第三，根据种子的定义，找出了任意数值半群的曾孙。RGD算法是目前已知最快的算法。但若将原始种子算法与RGD算法进行比较，可观察到种子算法使用了更精密的数学工具，而RGD算法使用了更适配最终C语言实现的数据结构。对于小于原生整数最大位宽约一半的亏格，新定义的种子算法性能显著优于RGD算法。对于未来允许更大原生整数位宽的编译器，这或将成为探索未达亏格半群树的强大工具。新种子算法除采用Fromentin和Hivert在该领域中巧妙引入的并行化与深度优先搜索等技术外，还运用了按位整数运算、最多含三个左侧元素的半群种子知识以及任意数值半群的曾孙特性。该算法已用于证明亏格为$66$时不存在Eliahou半群，从而验证了亏格不大于$66$时的Wilf猜想。我们还发现了三个亏格为$67$的Eliahou半群，其中有一个既非Eliahou-Fromentin型，也非Delgado型，但它属于Shalom Eliahou提出的一个新族群。