Balancelink : Partition Function 1.0

This script computes the partition function values 𝑝(𝑛) using Euler’s Pentagonal Number Theorem and displays them in a horizontally wrapped table directly on the chart. The partition function is a classic function in number theory that counts the number of ways an integer 𝑛 can be expressed as a sum of positive integers, disregarding the order of the summands.

Key Features
Efficient Calculation:
The script computes 𝑝(𝑛) for all orders from 0 up to a user-defined maximum (set by the "End Order" input). The recursive computation leverages Euler’s Pentagonal Number Theorem, ensuring the function is calculated correctly for each order.

Display Range Selection:
Users can select a specific range of orders (for example, from 𝑛 = 100 to 𝑛 = 200 to display.) This means you can focus on a particular segment of the partition function results without cluttering the chart.

Horizontally Wrapped Table:
The partition values are organized into a clean, horizontal table with a customizable number of columns per row (default is 20). When the number of values exceeds the maximum columns, the table automatically wraps onto a new set of rows for better readability.

Medium Text Size:
The table cells use a medium (normal) text size for easy viewing and clarity.

How to Use
Inputs:

Start Order (n): The starting index from which you want to display the partition function (default is 100).

End Order (n): The ending index up to which the partition function values will be displayed (default is 200).

Max Columns Per Row: Determines how many results are shown per row before wrapping to the next (default is 20).

Calculation:
The script calculates all 𝑝(𝑛) values from 0 up to the specified "End Order". It then extracts and displays only the values in the chosen range.

Visualization:
The computed values are shown in a neatly arranged table at the top right of your TradingView chart, making it simple to scroll through and inspect the partition function values.

Use Cases
Educational & Research:
Ideal for educators and students exploring concepts of integer partitions and number theory.

Data Analysis & Pattern Recognition:
Useful for those interested in the behavior and growth of partition numbers as 𝑛 increases.