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Semi-Latin squares have been extensively studied. They can be interpreted as a special case of latinized block designs where the number of columns is equal to the number of replicates in the design. Latinized row-column designs are…
We investigate sets of Mutually Orthogonal Latin Squares (MOLS) generated by Cellular Automata (CA) over finite fields. After introducing how a CA defined by a bipermutive local rule of diameter $d$ over an alphabet of $q$ elements…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
For Latin squares the units (rows and columns) have fixed sum. The same holds for rows, columns, and blocks in Sudokus. Summing the elements of a unit yields a linear equation, and the set of all such equations forms a system of linear…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
We introduce a direct numerical treatment of nonlinear higher-index differential-algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard…
In this paper, we study the rank of matrices of bicomplex numbers. The relationship between rank, idempotent column rank and idempotent row rank is examined. Then, the solution of a system of equations in bicomplex space is presented using…
We recall the Alon-Tarsi conjecture on the number of even latin squares. We introduce a map which switches the parity of a latin square under certain requirements. An example is included.
Do you want to know what an anti-chiece Latin square is? Or what a non-consecutive toroidal modular Latin square is? We invented a ton of new types of Latin squares, some inspired by existing Sudoku variations. We can't wait to introduce…
We report the results of a computer investigation of sets of mutually orthogonal latin squares (MOLS) of small order. For $n\le9$ we 1. Determine the number of orthogonal mates for each species of latin square of order $n$. 2. Calculate the…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Consider a partial Latin square $P$ where the first two rows and first three columns are completely filled, and every other cell of $P$ is empty. It has been conjectured that all such partial Latin squares of order at least $8$ are…
Two latin squares are orthogonal if, when they are superimposed, every ordered pair of symbols appears exactly once. This definition extends naturally to `incomplete' latin squares each having a hole on the same rows, columns, and symbols.…
Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…
Latin squares have been historically used in order to create statistical designs in which, starting from a small number of experiments, it can be obtained a large experimental space. In this sense, the optimization of the selection of Latin…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…
We provide formulas for the degrees of the projections of the locus of square matrices with given rank from linear spaces spanned by a choice of matrix entries. The motivation for these computations stem from applications to `matrix…