In this paper we define a new class of partially filled arrays, called $\lambda$-fold relative Heffter arrays, that are a generalization of the Heffter arrays introduced by Archdeacon in 2015. After showing the connection of this new concept with several other ones, such as signed magic arrays, graph decompositions and relative difference families, we determine some necessary conditions and we present existence results for infinite classes of these arrays. In the last part of the paper we also show that these arrays give rise to biembeddings of multigraphs into orientable surfaces and we provide infinite families of such biembeddings. To conclude, we present a result concerning pairs of $\lambda$-fold relative Heffter arrays and covering surfaces.

在本文中，我们定义了一类新的部分填充数组，称为 $\lambda$-fold 相对 Heffter 数组，这是 Archdeacon 在 2015 年引入的 Heffter 数组的概括。在展示了这个新概念与其他几个概念的联系后，例如有符号魔法数组、图分解和相对差异族，我们确定了一些必要的条件，我们给出了这些数组的无限类的存在结果。在论文的最后一部分，我们还展示了这些数组将多重图双嵌入到可定向曲面中，并且我们提供了此类双嵌入的无限族。总而言之，我们提出了一个关于成对的结果$\lambda$-折叠相对 Heffter 阵列和覆盖面。