Domino Antimagic Squares and Rectangles

Abstract A domino antimagic square of order n is an n × n array formed from a subset of the standard set of 28 dominoes such that the sums of the rows, columns, and two main diagonals form a set of 2 n + 2 distinct, consecutive integers while an m × n domino antimagic rectangle is an m × n rectangular array formed from a subset of the standard set of 28 dominoes such that the sums of the rows and columns form a set of m + n distinct, consecutive integers. This paper outlines what the possible dimensions are for m × n domino antimagic rectangles and provides many examples of both domino antimagic rectangles and squares. Many open questions are given at the end of the paper for future exploration.