👉 Shuffles are an important concept in probability theory and combinatorial mathematics, particularly in the context of generating functions. Essentially, a shuffle is an arrangement of objects that results in all possible outcomes of a random experiment. In other words, a shuffle can be thought of as a mathematical representation of a permutation.
Here's how shuffles work:
1.
Initial Condition
: We start with an initial set of objects (or elements) that we want to shuffle.
2.
Shuffle Step
: