# Enumerating multiplex juggling patterns

## TL;DR

This paper introduces a new combinatorial method using cards and embeddings of ordered partitions to enumerate multiplex juggling patterns, extending known results to more complex cases.

## Contribution

It presents a novel approach for enumerating multiplex juggling patterns using card-based embeddings, advancing beyond previous limited cases.

## Key findings

- Developed a card-based enumeration method for multiplex juggling
- Determined counts for small cases of multiplex juggling patterns
- Established combinatorial properties of the card sets used

## Abstract

Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any number of balls at a given time (known as multiplex juggling) the enumeration is more difficult and has only been established in a few special cases. We give a method of using cards related to "embeddings" of ordered partitions to enumerate the count of multiplex juggling sequences, determine these counts for small cases, and establish some combinatorial properties of the set of cards needed.