The Polyhedral Index Partition (PIP) and the Discovery of Pascal's Dimensions: Enabling Computational Retrieval and Reversibility in High-Index Partition Arrays
Listen to the paper: here
Author: Andrew Lehti
Disciplines: Cognitive Psychology, Linguistics, Mathematics, and their Histories
DOI: 10.6084/m9.figshare.27642783
The Polyhedral Index Partition (PIP) framework introduces an innovative approach to calculating integer partitions by leveraging the mathematical structures of Pascal's Triangle, specifically through the concepts of Pascal's Dimensions and Pascal's Laterals. This repository contains the Python implementation of PIP, which offers significant performance improvements over traditional partition enumeration methods.
- Python 3.8 or later
mpmath
library for arbitrary-precision arithmetic
Install mpmath
using:
pip install mpmath
Clone this repository to your local machine:
git clone https://github.com/andylehti/Polyhedral-Index-Partition.git
Run the Python script to compute partitions and their indices:
n = 55234587678685685685663467263573
p = 7
a = partition(n, p)
print("Partition:", a)
r = getInverse(*a)
print("Index:", r)
For more examples, see the notebook.
- Pascal, B. (1654). Traité du triangle arithmétique.
- Stanley, R. P. (1999). Enumerative Combinatorics.
- Sloane, N. J. A. (2003). The On-Line Encyclopedia of Integer Sequences.
Polyhedral Index Partition © Andrew Lehti, 2024