Author Archives: Peter Cameron

About Peter Cameron

I count all the things that need to be counted.

Algebraic properties of chromatic polynomials, 2

My paper with Kerri Morgan on algebraic properties of chromatic roots (described here) has just appeared in the Electronic Journal of Combinatorics: you can find it here. I won’t say any more about it, except to pose a challenge which … Continue reading

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Polynomials taking integer values

This is not a hot new result, just part of general mathematical culture. If a polynomial f(x) has integer coefficients, then its values at integer arguments are clearly integers. The converse is false; the simplest example is the polynomial x(x−1)/2. … Continue reading

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Apology

To my friends in the United States of America: I am sorry, but I do not expect I will be visiting you during the term of office of the current President. This for two reasons. First, I find his policies … Continue reading

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Reciprocity

The cycle index of a finite permutation group is a multivariate polynomial (with one variable si for each index i not exceeding the degree of the group) which is the generating function for the numbers of cycles of different lengths … Continue reading

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70

The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away. So today I … Continue reading

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Impact update

My comments on impact were cited by Ursula Martin and her co-author Laura Meagher here. Worth a look. PS Here’s the abstract: This empirical study explored how research can generate impacts by investigating different sorts of impacts from one academic … Continue reading

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Automorphism groups of transformation semigroups

I have been in the transformation semigroups game for nearly ten years now, but I still feel that I am finding my feet. Here is apparently a huge difference between permutation groups and transformation semigroups, one which is still not … Continue reading

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