Homogeneous Steiner triple systems

组合设计是将符号以满足特定条件的方式排列成图案。一个例子是数独，其中正方形阵列的每一行包含九个符号中的每一个，网格的每一列包含九个符号中的每一个，每个迷你正方形包含九个符号中的每一个。在数独游戏中，符号通常是数字1-9，但它们也可以是任何九个不同的符号，颜色等，因为重要的是排列，而不是实际的符号。斯坦纳三元系是另一种设计;这里一组符号被排列成三元组（三个符号的集合），以这样的方式，任何一对符号都正好出现在一个三元组中。在数学中，齐性是一种非常强的对称性，意味着任何局部对称实际上都是全局对称。该项目涉及有限和可数无限的Steiner三重系统，旨在对所有具有同质性的Steiner三重系统进行分类。

A combinatorial design is an arrangement of symbols into patterns in such a way that specified conditions are met. One example is a Sudoku, where each row of the square array contains each of the nine symbols exactly once, each column of the grid contains each of the nine symbols exactly once, and each mini-square contains each of the symbols exactly once. In a Sudoku the symbols are usually the numbers 1-9, but they could be any nine distinct symbols, colours, etc., since it is the arrangement that is important, not the actual symbols.A Steiner triple system is another type of design; here a set of symbols is arranged into triples (sets of three symbols) in such a way that any pair of the symbols occurs together in exactly one triple.In mathematics, homogeneity is a very strong symmetry property that means that any local symmetry is in fact a global symmetry. This project involves both finite and countably infinite Steiner triple systems and aims to work towards classifying all the Steiner triple systems with homogeneity properties.