Related papers: A new relationship between block designs
A preferential arrangement of a finite set is an ordered partition. Associated with each such ordered partition is a chain of subsets or blocks endowed with a linear order. The chain may be split into sections by the introduction of a…
Paul Erd\H{o}s and L\'aszl\'o Lov\'asz established that any \emph{maximal intersecting family of $k-$sets} has at most $k^{k}$ blocks. They introduced the problem of finding the maximum possible number of blocks in such a family. They also…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arrays, and transversal designs. Interest in constructing…
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the…
We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points such that every two blocks intersect each other in $\lambda$ points (and $\lambda < v$ is a fixed number) and…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
We propose a novel network formation game that explains the emergence of various hierarchical structures in groups where self-interested or utility-maximizing individuals decide to establish or severe relationships of authority or…
Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
We investigate random connected graphs from a block-stable class whose distribution is weighted based on the number of $2$-connected components, or blocks. This includes the class of planar graphs. For this, we develop a notion of a…
We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed…
(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree…
We develop a method to infer community structure in directed networks where the groups are ordered in a latent one-dimensional hierarchy that determines the preferred edge direction. Our nonparametric Bayesian approach is based on a…