Exact Enumeration of Five Dimensional Partitions

This is the homepage for the exact enumeration of five-dimensional partitions. The goal of this project is to carry out the exact enumeration of the numbers of five-dimensional partitions. We hope to add around 10-15 more numbers. This is sequence A000390 in the OEIS.

Results

Date Jan 2011
N 30
Code v1.0

Current state of the project: Ongoing

  • Jan 2011 Converted the code for solid partitions to compute five-dimensional partitions. This is v1.0 of the code. This generated the first 30 numbers. Nothing more was attempted as all efforts were towards pushing the solid partitions project.
  • June 10, 2011 Creating a parallel version of the code used to obtain the first 30 numbers.
  • Aug 2, 2011 Srivatsan completes the parallel version of the code. We hope to generate 10 more numbers after some preliminary tests are carried out to validate the code. With the runs for 4d partitions being completed, the timing couldn't have been more perfect.
  • Sept 27, 2011 The parallel code has bugs and hence no runs will be carried out until it is completely debugged.
  • Mar 2, 2012 Two new numbers are added using the new Bratley code!
(1)
\begin{align} \boxed{ p_5(31)=9385148192238 \quad,\quad p_5(32)=21684370682500} \ . \end{align}
  • [Mar 31, 2012] The next generation of code is being worked on. It will be an implementation of the Knuth algorithm with less memory usage and might run faster. Further, we are simultaneously working on a parallelization that works uniformly for partitions in all dimensions with tweaks for further speedup that is dimension dependent. These should be ready by the end of April 2012.

Code

  • v1.0 of the code is a straight port of the code that generated numbers for solid partitions.
  • v2.0 is a parallel version of the code. will not be developed any more
  • v3.0 see note of Mar 31, 2012 for details

Page maintained by Suresh Govindarajan

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