The Combinatorial Object Server

It looks like it is quite old, but I found the Combinatorial Object Server for the first time this week and I thought I’d share it with my readers. I was looking for irreducible polynomials with binary coefficients (don’t ask why) and I found that this server can generate them on the fly for you! A beautiful application of the web.

Here are some things it can do:

  • Permutations and their restrictions
  • Subsets or Combinations
  • Permutations or Combinations of a Multiset
  • Set Partitions
  • Numerical Partitions and relatives
  • Binary, rooted, free and other trees
  • Necklaces, Lyndon words, DeBruijn Sequences
  • Irreducible and Primitive Polynomials over GF(2) to GF(5)

This reminds me a bit of the famous Plouffe’s inverter which, given a floating point number, will give you a matching mathematical constant.

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Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

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