The following short article first arose as an Appendix to the paper Counting points of bounded height in monoid orbits, by WADE HINDES, which appears just above in this journal. Subsequently, due to the general nature of the underlying problem, we thought that the result could have further applications, and could be easily overlooked if it appeared as an appendix. So, with the welcome kind help of the Editors, we decided to publish the result separately.
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