Number cubes with consecutive line sums
Peter Dukes, Joanna Niezen
TL;DR
This paper investigates the existence of special number cubes with consecutive line sums, employing combinatorial block designs and graph decompositions to establish their existence for specific cases.
Contribution
It introduces new methods using combinatorial designs and graph theory to solve the problem of anti-magic cubes with consecutive line sums.
Findings
Existence of certain anti-magic cubes confirmed.
Construction methods for small examples provided.
Application of combinatorial block designs demonstrated.
Abstract
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Coding theory and cryptography