论文标题
在$λ$ - 倍相的相对heffter阵列和表面上的多绘画
On $λ$-fold relative Heffter arrays and biembedding multigraphs on surfaces
论文作者
论文摘要
In this paper we define a new class of partially filled arrays, called $λ$-fold relative Heffter arrays, that are a generalisation 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.在本文的最后一部分中，我们还表明，这些阵列会导致多数形式的生物床形成可定向的表面，并且我们提供了此类生物床的无限家族。总而言之，我们提出了有关$λ$倍的相对heffter阵列和覆盖表面的结果。
In this paper we define a new class of partially filled arrays, called $λ$-fold relative Heffter arrays, that are a generalisation 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 $λ$-fold relative Heffter arrays and covering surfaces.
