Number Cubes with Consecutive Line Sums

Abstract

We settle the existence of certain “anti-magic” cubes using combinatorial block designs and graph decompositions to align a handful of small examples.

MSC:

• Primary 05B07
• Secondary 05C70

Acknowledgment

We are grateful to the referees for their careful reading and several good suggestions, which helped improve the presentation. The research of the first author is supported by NSERC grant 312595–2017.

Additional information

Funding

Natural Sciences and Engineering Research Council of Canada;

Notes on contributors

Peter J. Dukes

Peter Dukes received his Ph.D. in mathematics from Caltech in 2003. He joined the University of Victoria as a faculty member in 2004. He enjoys the interplay between combinatorics and other areas of mathematics, such as linear algebra and number theory.

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 2Y2

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Joanna Niezen

Joanna Niezen received her Ph.D. in mathematics from the University of Victoria in September 2020. She now works at Simon Fraser University as a lecturer in the department of mathematics. She brings an enthusiasm for research to the classroom. While doing her graduate studies, Joanna was the president of three student groups at the University of Victoria: the student union for all graduate-level mathematics and statistics students, the Association for Women in Math UVic Student Chapter, and the UVic Artistic Swimming Club.

Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6

[email protected]