Dr Cian O'Brien

قبول طلاب الدكتوراة

مشروعات الدكتوراة

"Alternating Sign Hypermatrices and Characterisations of Latin-like Squares":

Alternating sign matrices are a class of matrices with deep connections to a wide variety of areas in mathematics and beyond. A Latin square is an n×n grid containing numbers from {1, 2, ..., n} with each number occurring exactly once in each row and column. A Sudoku puzzle is a well known example. A connection has recently been made between Latin squares and a 3-dimensional version of alternating sign matrices called an alternating sign hypermatrix (ASHM). At present, these Latin-like squares can only be recognised by finding the corresponding ASHM, and there is no known set of necessary and sufficient rules for what its entries can be. After some introductory study of these objects, the aim of this project would be to find further necessary conditions on the entries of a Latin-like square.