Partition identities, functional equations and computer algebra

By Jehanne Dousse

Appears in collection : 2023 - T3 - WS3 - Computer algebra for functional equations in combinatorics and physics

A partition of a positive integer $n$ is a non-increasing sequence of positive integers whose sum is $n$. A partition identity is a theorem stating that for all $n$, the number of partitions of $n$ satisfying some conditions equals the number of partitions of $n$ satisfying some other conditions. In this talk, we will show how functional equations and computer algebra can be used to prove such identities. In particular we will discuss a semi-automatic method using recurrences and $q$-difference equations, and what would be needed to make it fully automatic.

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Citation data

  • DOI 10.57987/IHP.2023.T3.WS3.014
  • Cite this video Dousse, Jehanne (08/12/2023). Partition identities, functional equations and computer algebra. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T3.WS3.014
  • URL https://dx.doi.org/10.57987/IHP.2023.T3.WS3.014

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