发表机构
Universitat de Lleida; Universitat Politècnica de Catalunya; Barcelona Graduate School of Mathematics; Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech)（莱里达大学; 加泰罗尼亚理工大学; 巴塞罗那数学研究生院; UPC-巴塞罗那理工大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入一类与循环群相关的四分之三循环有向图，通过限制生成元组合至三个扇区，利用格点与镶嵌分析可达集增长，给出Moore型上界、显式构造及计算实验，揭示约束格点与极值问题的联系。
AI 中文摘要
我们引入并研究了一类与循环群$\Z_N$相关联的新的循环有向图族，该族通过将两个生成元$a$和$b$的允许组合限制在三个坐标扇区中获得。由此产生的类距离函数不同于循环有向图中的标准有向距离，并引发了新的几何与组合现象。利用平面格点表示和周期镶嵌，我们分析了可达集的增长，并推导了相应的阶/直径问题的Moore型上界。我们构造了具有指定直径的四分之三循环结构的显式无限族，并提供了确定允许生成元对的基于格点的方法。对于偶数直径和奇数直径分别获得了不同的构造。此外，针对小阶和中阶的计算实验表明，偶数直径存在改进的族，并激发了一个关于最大可达阶的猜想渐近公式。本文强调了约束格点表示、周期镶嵌与循环网络极值问题之间的相互作用。
英文摘要
We introduce and study a new family of circulant digraphs associated with the cyclic group $\Z_N$, obtained by restricting admissible combinations of two generators $a$ and $b$ to three coordinate sectors. The resulting distance-like function differs from the standard directed distance in circulant digraphs and gives rise to new geometric and combinatorial phenomena. Using planar lattice representations and periodic tessellations, we analyze the growth of reachable sets and derive Moore-type upper bounds for the corresponding order/diameter problem. We construct explicit infinite families of three-quarters circulant structures with the prescribed diameter and provide lattice-based methods for determining admissible generator pairs. Separate constructions are obtained for even and odd diameters. In addition, computational experiments for small and moderate orders suggest improved families for even diameters and motivate a conjectural asymptotic formula for the maximum attainable order. The paper highlights the interplay between constrained lattice representations, periodic tilings, and extremal problems for circulant networks.
