论文标题
天然的quasirandomness特性
Natural quasirandomness properties
论文作者
论文摘要
quasirandomness的理论已从其首发理论环境大大扩展到几种不同的组合对象，例如超图，锦标赛，排列等。但是，这些quasirandomness变体已经以临时的逐一案例方式完成。在本文中，我们提出了quasirandomness属性的三个新层次结构，可以自然定义为任意组合对象。从更正式的意义上讲，我们的属性也是“自然的”：它们由当地组合结构（按开放的解释编码）保存。我们表明，我们的quasirandomness属性具有几种不同但等效的特征，类似于超图准词素特性。我们还证明了几种含义和分离，将它们相互比较，以及对超图已知的内容。 我们的陈述和证据探讨的主要概念是独特的耦合性：如果组合理论中存在一个唯一的极限对象，则两个限制对象是唯一耦合的，这是这两个对象的对齐（即，耦合）。
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have been done in an ad-hoc case-by-case manner. In this paper, we propose three new hierarchies of quasirandomness properties that can be naturally defined for arbitrary combinatorial objects. Our properties are also "natural" in more formal sense: they are preserved by local combinatorial constructions (encoded by open interpretations). We show that our quasirandomness properties have several different but equivalent characterizations that are similar to hypergraph quasirandomness properties. We also prove several implications and separations comparing them to each other and to what has been known for hypergraphs. The main notion explored by our statements and proofs is that of unique coupleability: two limit objects are uniquely coupleable if there is a unique limit object in the combined theory that is an alignment (i.e., a coupling) of these two objects.
