Sequential Stub Matching for Asymptotically Uniform Generation of Directed Graphs with a Given Degree Sequence [0.03%]
有向图的逐次匹配法及其给定度序列图形均匀生成渐进性研究
Femke van Ieperen,Ivan Kryven
Femke van Ieperen
We discuss sequential stub matching for directed graphs and show that this process can be used to sample simple digraphs with asymptotically equal probability. The process starts with an empty edge set and repeatedly adds edges to it with a...
Florian Schreier-Aigner
Florian Schreier-Aigner
We introduce a symmetry class for higher dimensional partitions-fully complementary higher dimensional partitions (FCPs)-and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define varia...
On Graphs Embeddable in a Layer of a Hypercube and Their Extremal Numbers [0.03%]
关于可嵌入超立方体一层中的图及其极值数量
Maria Axenovich,Ryan R Martin,Christian Winter
Maria Axenovich
A graph is cubical if it is a subgraph of a hypercube. For a cubical graph H and a hypercube Q n , ex ( Q n , H ) is the largest number of edges in an H-free subgraph of Q n . If ex ( Q n , H ) is at least a positive proportion of the n...
Katharina T Huber,Vincent Moulton,Megan Owen et al.
Katharina T Huber et al.
An equidistant X-cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X, that is used in biology to represent the evolutionary history of a set X of species. In this paper, we introduce and investigate the space of...
Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions [0.03%]
拉马努金的theta函数与划分的零件和扭曲的奇偶性
Koustav Banerjee,Manosij Ghosh Dastidar
Koustav Banerjee
In this paper, we explore intricate connections between Ramanujan's theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a p...
Pattern Hopf Algebras [0.03%]
模式Hopf代数
Raul Penaguiao
Raul Penaguiao
In this paper, we expand on the notion of combinatorial presheaf, first introduced explicitly by Aguiar and Mahajan in 2010 but already present in the literature in some other points of view. We do this by adapting the algebraic framework o...
Manfred Buchacher,Sophie Hofmanninger,Manuel Kauers
Manfred Buchacher
We provide some first experimental data about generating functions of restricted lattice walks with small steps in N 4 . © The Author(s) 2021.
Interval Graph Limits [0.03%]
区间图极限
Persi Diaconis,Susan Holmes,Svante Janson
Persi Diaconis
We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, ...