User:Raul M. Falcon

My current research involves the use of Gröbner bases in order to study the distribution of k x n partial Latin rectangles, that is, k x n arrays in which each cell is either empty or contains one element chosen from a set of n symbols, such that each symbol occurs at most once in each row and in each column. Such a distribution generalizes that of Latin rectangles (partial Latin squares without empty cells), which is known for order up to 11 and have applications in some domains where they constitute an important tool, like, for instance, Statistics, Design of Experiments, Scheduling, Cryptography or Social Networks. I am also interested in 3-seminets, which are uniquely related to the main classes of partial Latin rectangles and generalize the traditional concept of net.