A *signed magic rectangle SMR*(*m,n*;*k,s*) is an *m *× *n *array with entries from *X*, where *X *= {0*,*±1*,*±2*,..., *±(*mk*−1)*/*2} if *mk *is odd and *X *= {±1*,*±2*,...,*±*mk/*2} if *mk *is even, such that

- precisely
*k*cells in every row and*s*cells in every column are filled, - every integer from set
*X*appears exactly once in the array, and - the sum of each row and of each column is zero.

In this seminar we first present a brief history of signed magic rectangles. Then the results obtained on the existence of an *SMR*(*m,n*;*k,s*) are presented.

Joint work with David Leach and Brandi Ellis, UWG.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

#### Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

#### Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar or Travis Scrimshaw.