论文标题
拉丁矩形的半魔法正方形的晶格路径枚举
Lattice path enumeration for semi-magic squares by Latin rectangles
论文作者
论文摘要
类似于标准的年轻tableaux如何代表年轻晶格中的路径，拉丁矩形可能被用来枚举半魔法正方形的Poset中的路径，而条目零或一个。与确定性相关的对称性保留此poset，我们完全描述了尺寸4、5和6的正方形的轨道，涵盖数据和最大链。在这些情况下，最后一项给出了拉丁正方形的数量。为了有效地计算尺寸6，我们依次识别具有某些等效类别超图的轨道。
Similar to how standard Young tableaux represent paths in the Young lattice, Latin rectangles may be use to enumerate paths in the poset of semi-magic squares with entries zero or one. The symmetries associated to determinant preserve this poset, and we completely describe the orbits, covering data, and maximal chains for squares of size 4, 5, and 6. The last item gives the number of Latin squares in these cases. To calculate efficiently for size 6, we in turn identify orbits with certain equivalence classes of hypergraphs.
