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I am reading a textbook which uses the LaTeX \smile symbol (a sort of sideways parenthesis) for concatenation of lists. I have never seen this symbol anywhere before except in the document which lists all LaTeX symbols. It may be that this use of \smile for concatenation is standard, and has passed me by. I myself either simply use + for concatenation, or if in pseudo code write it out in words.

Anyway, I'm just curious as to this use of the smile symbol.

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It is very common in Mathematics, more specific in Algebraic Topology. It is used to denote the cup product.

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  • There is also the rather lazy alternative $\cup$ for this, which would seem to be correct based on the name. I never got that.
    – Ryan Reich
    Oct 17, 2013 at 2:42
  • @RyanReich, in old texts we can see the cup symbol being used to cup products. But nowadays we have this better option and cup is used for unions.
    – Sigur
    Oct 17, 2013 at 2:45
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    Thanks: cup product it is. (My own knowledge of algebraic topology never advanced very far beyond elementary undergraduate material.) Maybe since \cup is used for unions, the "cup product" should be re-named the "smile product"!
    – Alasdair
    Oct 17, 2013 at 5:40
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    @Sigur I see \cup usd in newly written documents all the time. It's the name, I believe. And lack of interest in learning of the numerous subtly different alternatives when a decent default exists. I agree that the cup, being dual to an actual intersection pairing in homology, is "a kind of union", which explains at least the shape of the symbol, if not its precise proportions.
    – Ryan Reich
    Oct 17, 2013 at 16:08
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    \smile positioned on the baseline occurs also in performance scores of musical settings of poems or religious verse where it is used at the end of a line or text to denote a "carry-over" to the next line or phrase with no pause or breath.
    – Peter Flynn
    Nov 7, 2018 at 22:03

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