### Top Posts

### Recent comments

### Blogroll

- Alexander Konovalov
- Annoying precision
- Astronomy Picture of the Day
- Azimuth
- Bad science
- Bob Walters
- British Combinatorial Committee
- CIRCA tweets digest
- CoDiMa
- Coffee, love, and matrix algebra
- Computational semigroup theory
- DC's Improbable Science
- Diamond Geezer
- Exploring East London
- From hill to sea
- Gödel's lost letter and P=NP
- Gil Kalai
- Haris Aziz
- Intersections
- Jane's London
- Jon Awbrey
- LMS blogs page
- Log24
- London Algebra Colloquium
- London Reconnections
- Marie Cameron's blog
- MathBlogging
- Micromath
- Neill Cameron
- neverendingbooks
- Noncommutative geometry
- numericana hall of fame
- Paul Goldberg
- Robert A. Wilson's blog
- Sheila's blog
- Since it is not …
- Spitalfields life
- St Albans midweek lunch
- Stubborn mule
- Sylvy's mathsy blog
- SymOmega
- Tangential thoughts
- Terry Tao
- The Aperiodical
- The De Morgan Journal
- The ICA
- The London column
- The Lumber Room
- The matroid union
- Theorem of the day
- Tim Gowers
- Vynmath
- XKCD

### Find me on the web

### Cameron Counts: RSS feeds

### Meta

# Author Archives: Peter Cameron

## 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

Posted in open problems, Uncategorized
Tagged algebraic integer, chromatic polynomial, Galois group
2 Comments

## 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

Posted in exposition
Tagged difference polynomials, integers, polynomials, reciprocal polynomials
4 Comments

## 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

Posted in Uncategorized
4 Comments

## 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

Posted in exposition
Tagged Bill Jackson, cycle polynomial, Jason Rudd, Jason Semeraro, orbital chromatic polynomial
1 Comment

## 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

## 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

## 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

Posted in doing mathematics, open problems, Uncategorized
Tagged automorphism, primitive groups, synchronization
Leave a comment