Dr Dave COULSON

Fellow (Associate)

School of Mathematics and Statistics

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Research Interests

  • The polychromatic number of 3-space
  • The chromatic number of 2-space
  • The chromatic number of 3-space

Research Groups

Extra Information

We say that we have a chromatic colouring of n-space if we assign each point of n-space to a set and there is some distance d (an excluded distance) so that no two points in the same set are distance d apart. The minimum number of sets needed is known as the chromatic number of n-space. At the moment it is known only that the chromatic number of two space lies between 4 and 7 (inclusive) and that the chromatic number of three space lies between 5 and 15 (inclusive). A polychromatic colouring of n-space is similar to a chromatic colouring of n-space but we allow each set to have an excluded distance that is different from another set (rather than a common one d). There are polychromatic colourings of 2-space with 6 sets bettering the most efficient known chromatic colouring with 7 sets. It is not known whether 3-space admits a polychromatic colouring with less than 15 sets (the number of sets in the most efficient chromatic colouring of 3-space uses 15 sets).

Past Postgraduate Supervision

Name Thesis title
Ashish GUPTA "Irreducible representations of some classes of quantum laurent polynomials"

Past MSc Students

Name Project title
Benjamin FLEMING "Quantizing properties of the 12-16 partition of 3-space"
Candice RABUSA