Related papers: Enumeration of Row-Column Designs

Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above…

We note that a rational $3$-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational $3$-tangle diagrams up to isotopy. However, there is no perfect classification about rational…

Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of…

We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…

We call a real multi-dimensional array a {\em tensor} for short. In enumerating vertices of the polytopes of stochastic tensors, different approaches have been used: {(1)} Combinatorial method via Latin squares; {(2)} Analytic (topological)…

In an array of random variables, each row can be regarded as a single, sequence-valued random variable. In this way, the array is seen as a sequence of sequences. Such an array is said to be row exchangeable if each row is an exchangeable…

We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.

Motivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank $r$ and with bounded subdeterminants. In particular, we study the…

In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…

We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are…

The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescription of some of the four types of invariants that form the…

We investigate the existence of heavy columns in binary matrices with distinct rows. A column of an m x n binary matrix is called heavy if the number of ones in it is at least m/2. We introduce two recursive algorithms, A1 and A2, that…

The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, called the \emph{Sinkhorn limit} of $A$. Exact formulae for the Sinkhorn…

We study two kinds of generalizations of symmetric block designs to higher dimensions, the so-called $\mathcal{C}$-cubes and $\mathcal{P}$-cubes. For small parameters, all examples up to equivalence are determined by computer calculations.…

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline…

We show that there is a dense set $\ourset\subseteq \mathbb{N}$ of group orders and a constant $c$ such that for every $n\in \ourset$ we can decide in time $O(n^2(\log n)^c)$ whether two $n\times n$ multiplication tables describe isomorphic…

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…

We have performed a complete enumeration of non-isotopic triples of mutually orthogonal $k\times n$ Latin rectangles for $k\leq n \leq 7$. Here we will present a census of such triples, classified by various properties, including the order…

We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…

In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…