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Say we have some (geometric) object, let it be a binary tree $T$. Say we have a map $f$ which rotates $T$ at some certain nodes, let's say that it rotates the tree at the nodes labelled by odd numbers (assume that labelling\relabelling after rotation etc. has been appropriately fixed beforehand). Can I then say that $f$ acts on $T$ (via rotating etc. etc.)? Is such abuse of notation tolerated and understood?

billy192
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  • I don’t see how it’s an abuse. – Kevin Carlson Jan 21 '20 at 13:58
  • We usually use the term "acting" when we talk about group acting on some set, object or a ring acting on a group, etc. I was unsure if it was correct to use that term in relation with a map, even though the meaning is clear. – billy192 Jan 21 '20 at 14:19
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    Well, for instance, you could say that the monoid generated by $f$ and its self-compositions acts on the graph. But I see no reason not to apply the terminology to a single map. – Kevin Carlson Jan 21 '20 at 14:21
  • Ok, thank you @KevinCarlson – billy192 Jan 21 '20 at 14:36

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