论文标题
平衡列出的多编码和整数矩阵的副本
Balancing permuted copies of multigraphs and integer matrices
论文作者
论文摘要
给定整数上方的方形矩阵$ a $，我们考虑$ \ mathbb {z} $ - 模块$ m_a $由所有置换矩阵产生的集合类似于$ a $。在签名的图形分解和块设计上，我们对完全对称的矩阵$ a i + b j $属于$ m_a $感兴趣。我们提供了一种相对快速的方法来计算此类矩阵的发电机，避免了在$ \ Mathbb {z} $上使用非常大的规范形式的需求。我们详细考虑了几种特殊情况。特别是，对称矩阵的问题回答了Cameron和Cioabǎ确定整数的最终期限$λ$的问题，以便$λ$ - 折叠完整的完整图$λk_n$在给定（multi）图中具有边缘分解。
Given a square matrix $A$ over the integers, we consider the $\mathbb{Z}$-module $M_A$ generated by the set of all matrices that are permutation-similar to $A$. Motivated by analogous problems on signed graph decompositions and block designs, we are interested in the completely symmetric matrices $a I + b J$ belonging to $M_A$. We give a relatively fast method to compute a generator for such matrices, avoiding the need for a very large canonical form over $\mathbb{Z}$. We consider several special cases in detail. In particular, the problem for symmetric matrices answers a question of Cameron and Cioabǎ on determining the eventual period for integers $λ$ such that the $λ$-fold complete graph $λK_n$ has an edge-decomposition into a given (multi)graph.
