We present a new algorithm to explore or count the numerical semigroups of a given genus which uses the unleaved version of the tree of numerical semigroups. In the unleaved tree there are no leaves rather than the ones at depth equal to the genus in consideration. For exloring the unleaved tree we present a new encoding system of a numerical semigroup given by the gcd of its left elements and its shrinking, that is, the semigroup generated by its left elements divided by their gcd. We show a method to determine the right generators and strong generators of a semigroup by means of the gcd and the shrinking encoding, as well as a method to encode a semigroup from the encoding of its parent or of its predecessor sibling. With the new algorithm we obtained $n_{76}=29028294421710227$.

翻译：本文提出了一种探索或计数给定亏格数值半群的新算法，该算法采用数值半群树的未剪枝版本。在未剪枝树中，除深度等于所考虑亏格的节点外不存在叶节点。为探索未剪枝树，我们提出了一种新的数值半群编码系统，该系统由其左元素的最大公约数及其收缩（即由其左元素除以它们的最大公约数生成的半群）给出。我们展示了通过最大公约数和收缩编码确定半群的右生成元与强生成元的方法，以及从其父节点或前驱兄弟节点的编码推导半群编码的方法。利用新算法，我们得到了$n_{76}=29028294421710227$。