Partitions are studied in the mathematical fields of number theory and combinatorics, but have applications in many other areas, such as algebraic geometry, theoretical physics, and representation theory, where partitions arise in the study of monomial ideals, symmetric polynomials, special eigenfunctors and operators, and irreducible representations of symmetric groups to name a few.
This tutorial gives a subjective view on the theory of integer partitions, along with sample code for calculations using SageMath.
It is intended to be useful both for those interested in learning more about the combinatorics of partitions (along with some applications), as well as those wanting to learn how to use SageMath for combinatorial calculations.
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SageMath is a free open-source mathematics software system using a Python-based language which you can download and install for yourself, or simply run online or in the cloud. We will demonstrate some functionality of SageMath’s module for integer partitions (tutorial, documentation, source), but hopefully improve on the documentation already available by providing an accessible, illustrated, and interactive explanation of the mathematical background at the same time.
If you want to learn more about the multitude of other uses of SageMath for mathematical computations, check out their extensive documentation.
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Hi! My name is Edward and I am the author of this tutorial. If you want to find out more about me or get in touch, you can check out my personal website. If you like what you are reading please consider donating (link in menu) so I can continue creating educational content.