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Say I want to make clear that, say, the index $i$ on a symbol always means "initial configuration", or the "hat" $\hat{}$ always stands for "maximum". What I've seen a couple times is the notation bracket \cdot bracket, as in

  • "$(\cdot)_i$ means the initial configuration of $(\cdot)$"
  • "$\hat{(\cdot)}$ is the maximum of $(\cdot)$"

I'm wondering if there is a special symbol better than $(\cdot)$ (which feels kinda improvised), or if there are other, cleaner ways to write this?

MaxD
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    It's a placeholder. You could replace this with a free variable, say $x$ or any symbol not obviously used for other purposes. It doesn't matter as long as the notation is understandable. For instance, it's not mathematically wrong to declare $(\cdot)$ to be a variable and write $\int \exp (\cdot)\mathrm d(\cdot)$, but it would be more customary to use $x$ instead. Likewise, I see sometimes $x$ use as an integer index variable for a sequence $u_x=\dots$, while $n$ or $i$ would be considered more usual. – Jean-Claude Arbaut Apr 09 '22 at 08:04

1 Answers1

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To be honest, I would not recommend writing $\hat X$ for the max of $X$, since $\max X$ is the usual notation. That said, it would be clearer to simply write something like

For each $X$, let $(X)_i$ denote its initial configuration and $\widehat X$ his maximum.

J.-E. Pin
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