# 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} }

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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