The Magic of Summation Sequences Applied Combinatorics and Graph Theory

Abstract

Mathematics is a useful basis for motivating self-working card tricks. In this paper, we expand the realm of self-working magic tricks through the examination of a novel type of universal cycle called a Summation Sequence. An analysis of the graph theoretical and combinatorial structure of Summation Sequences reveals, firstly, the existence of operations that preserve the properties of Summation Sequences, and, secondly, a special type of Summation Sequence called a Symmetric Sequence. We apply our most important results to the realm of card magic, where we exploit the properties of Summation Sequences to motivate various card effects.