If we consider $n$ different polynomials in the Euclidean plane that intersect at some point, we can describe a permutation of the set $\{1,...,n\}$ by observing the values of the polynomials at the points to the left and right of the intersection. The permutations we get in this way are called interchanges. We prove that the set $a(n)$ of all interchanges of $n$ polynomials is smaller than the set $S(n)$ of all permutations of $n$ elements. Furthermore, we clarify exactly which permutations are interchanges. To do this, we use pruned trees, a subset of trees with the property that each interchange defines a unique pruned tree and each pruned tree is defined by some interchange. Therefore, we find a bijective function between the set of interchanges and the set of pruned trees. Finally, we observe some of the characteristics of the sequence $a(n)$.
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