Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds

Enumeration and random realization of triangulated surfaces

We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.

Lexicographic Enumeration of Set Partitions

In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in modern high-level programming languages, without recursive structures and jump logic. We show that they require linear space in respect to the set cardinality and advance the enumeration in constant amortized time. The methods discussed in this document are not novel. Our goal is to demonstrate the process of enumerating set partitions and highlight the ide…

Decomposition and Enumeration of Triangulated Surfaces

We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions and genus-surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most a fixed number of vertices. We specialize the theory for the case where the number of vertices is at most 11 and we get theoretical restrictions on genus-surfaces allowing us to get the list of triangulations of closed surfaces with at most 11 vertices.

Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I

We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.

用于枚举电路、余电路和三角剖分直至对称的对称字典序对称子集反向搜索

Symmetric lexicographic symmetric-subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry

研究利用对称字典序对称子集反向搜索框架枚举有限集对称可行子集，针对余电路、电路和三角剖分应用提出新方法，经C++实现后大幅提速，还计算出多个新数量并发现相关实例问题。

通过并行有界字典流实现数值半群中 GPU 加速的因子分解集

GPU-accelerated factorization sets in numerical semigroups via parallel bounded lexicographic streams

针对数值半群元素因子分解集的枚举问题，提出利用界并行化字典序枚举的方法，支持 GPU 与分布式计算，并提供带实测运行时间的 CUDA 实现。