Plane-filling curves on all uniform grids

网格着色上的边覆盖平面填充曲线：一种直观方法

Edge-covering plane-filling curves on grid colorings: a pedestrian approach

本文研究正多边形平面铺嵌上的边覆盖平面填充曲线，通过将铺嵌对称群的边类划分为对应于有限子群的精化着色，构造出称为曲线集的平面填充曲线族，并以图示示例直观展示。

分形龙形空间填充折叠曲线边界的L-系统

L-systems for the Boundaries of fractal dragon space filling folding curves

本文提出一种算法，可为分形龙形等方形网格空间填充折叠曲线的边界自动构造L-系统，补充了Dekking、Arndt和Handl在空间填充曲线方面的研究。

用多项式覆盖均匀网格的权重确定集

Covering Weight-Determined Sets of Uniform Grids by Polynomials

该研究确定了特征零域上覆盖均匀网格权重确定子集的非零多项式的最小次数，将此前仅适用于严格单峰均匀网格的结果推广到所有均匀网格，借助有限次数扎里斯基闭包等工具实现了组合表征。

Uniform hypergraphs containing no grids

A hypergraph is called an r by r grid if it is isomorphic to a pattern of r horizontal and r vertical lines. Three sets form a triangle if they pairwise intersect in three distinct singletons. A hypergraph is linear if every pair of edges meet in at most one vertex. In this paper we construct large linear r-hypergraphs which contain no grids. Moreover, a similar construction gives large linear r-hypergraphs which contain neither grids nor triangles. For r at least 4 our constructions are almost optimal. These investigations are also motivated by coding theory: we get new bounds for optimal sup…

Lattice structure of Grid-Tamari orders

The Tamari order is a central object in algebraic combinatorics and many other areas. Defined as the transitive closure of an associativity law, the Tamari order possesses a surprisingly rich structure: it is a congruence-uniform lattice. We consider a larger class of posets, the Grid-Tamari orders, which arise as an ordering on the facets of the non-kissing complex introduced by Pylyavskyy, Petersen, and Speyer. In addition to Tamari orders, some interesting examples of Grid-Tamari orders include the Type A Cambrian lattices and Grassmann-Tamari orders. We prove that the Grid-Tamari orders ar…

均匀仿射网格网络中的Braess悖论

Braess' Paradox in Uniform Affine Grid Networks

本文研究均匀仿射矩形网格网络中的Braess悖论，给出引发悖论的充要条件，计算相关弦的占比，改进Braess比率上界并证明比率最大化弦的延迟特性。