# Combinatorial cycles of a polynomial map over a commutative field

```@article{Chass1986CombinatorialCO,
title={Combinatorial cycles of a polynomial map over a commutative field},
author={G. Chass{\'e}},
journal={Discret. Math.},
year={1986},
volume={61},
pages={21-26}
}```
• G. Chassé
• Published 1986
• Computer Science, Mathematics
• Discret. Math.
Abstract Let K be a commutative field and f : K → K a polynomial map. We show that, if the degree of f as a polynomial is greater than 1, then the cycle length of f , extended to an algebraic closure K of K is not bounded. That is to say that, for each positive integer N , one can find an integer n , n ⩾ N such that there exist n different elements x 1 ,…, x n of K with the property: f ( x i ) = x i +1 for i , 1⩽ i ⩽ n − 1 and f ( x n ) = x 1 .
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