On polynomials which commute with a given polynomial

Author:
William M. Boyce

Journal:
Proc. Amer. Math. Soc. **33** (1972), 229-234

MSC:
Primary 12D99

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291138-3

MathSciNet review:
0291138

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Abstract | References | Similar Articles | Additional Information

Abstract: By extending a theorem of Jacobsthal, the following result is obtained: if *g* is a nonlinear polynomial, there is an integer such that for each there are either or zero distinct polynomials of degree *m* which commute with *g*. A formula is given for computing from the coefficients of *g*.

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DOI:
https://doi.org/10.1090/S0002-9939-1972-0291138-3

Keywords:
Commuting functions,
commuting polynomials,
common fixed point,
Tchebycheff polynomials,
functional composition

Article copyright:
© Copyright 1972
American Mathematical Society