论文标题
一类高度对称的大主教嵌入
A class of highly symmetric Archdeacon embeddings
论文作者
论文摘要
大主教在他的开创性论文$ [1] $中定义了Heffter Array的概念，以提供完整图$ k_v $的Biembeddings的明确构造中，即在可定位的表面，即所谓的大巨星嵌入式中，并证明这些嵌入是$ \ Mathbb {z} $ forights $ {z} $ - {v} $ - 在本文中，我们表明，大主教的嵌入可能会允许一个严格大于$ \ Mathbb {z} _ {V} $的自动构态组。的确，作为Buratti最近在$ [2] $中引入的有趣类阵列的应用，我们展示了无限的$ v $值，这是这种类型的嵌入这种类型的，具有完整的自动形态大小$ {v \ select 2} $，这是最大可能的一个。
Archdeacon, in his seminal paper $[1]$, defined the concept of Heffter array to provide explicit constructions of biembeddings of the complete graph $K_v$ into orientable surfaces, the so-called Archdeacon embeddings, and proved that these embeddings are $\mathbb{Z}_{v}$-regular. In this paper, we show that an Archdeacon embedding may admit an automorphism group that is strictly larger than $\mathbb{Z}_{v}$. Indeed, as an application of the interesting class of arrays recently introduced by Buratti in $[2]$, we exhibit, for infinitely many values of $v$, an embedding of this type having full automorphism group of size ${v \choose 2}$ that is the largest possible one.
