The Partitions Project

This is the home page of the partitions project. The goal is to understand various aspects of higher-dimensional partitions such as

  1. History of higher-dimensional partitions
  2. their exact enumeration;
  3. refined counting of higher-dimensional partitions
  4. their asymptotic behaviour and
  5. theoretical aspects of partitions.
  6. Links to partitions related stuff

Can you help this project?

We anticipate that there will be significant contributions from undergraduate students to this project. Contributions can be in the form of code, algorithms or theoretical insights. If you are an undergraduate student and wish to contribute to this project, send an email to solidpartitions at

Summer Interns

Summer 2014 sees two undergraduate students, Utkarsh Simha (PES U., Bangalore) and Neeraja Abhyankar (IIT Madras), working on the partitions project.

Anyone willing to spend Summer 2019 on this project?

Projects currently active: Unimodality of Partitions, Exact enumeration of 4-dim partitions. However, you are welcome to pick anything that interests you.


While the goal of the project is to have fun while explicitly enumerating partitions, occasionally there is a result that might be worth publishing.

  1. S. Balakrishnan, S. Govindarajan and N. S. Prabhakar, On the asymptotics of higher-dimensional partitions, J.Phys.A A45 (2012) 055001 arXiv:1105.6231
  2. S. Govindarajan, Notes on higher-dimensional partitions J. of Combinatorial Theory, Ser. A 120 (3) (2013) 600-622 arXiv:1203.4419
  3. S. Govindarajan and N. S. Prabhakar, A superasymptotic formula for the number of plane partitions, arXiv:1311.7227
  4. N. Destainville and S. Govindarajan, Estimating the asymptotics of solid partitions, J. Stat. Phys. 158 (2015) 950 arXiv:1406.5605
  5. S. Govindarajan, A. Guttmann and V. Subramanyan, On a square-ice analogue of plane partitions, arXiv:1607.01890

This page is maintained by Suresh Govindarajan

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