# What is the symbol “between” (≬) used for?

The `amssymb` package has a binary relation symbol named `\between`, which I have never come across.

What is it used for?
I found out from a compiler error when I tried to define a symbol named that way myself, and I am now wondering whether it is a symbol I could use for my purpose.

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I wonder if there is any efficient way to find all ArXiv papers that contain `\between` in their Latex source code? –  Jukka Suomela Nov 1 '10 at 9:23
This is an interesting question, and I'm curious to find the answer, but I can't help it would be better placed at the mathematics stackexchange: It's not really a question about LaTeX... math.stackexchange.com –  Seamus Nov 1 '10 at 11:39
Never seen it before. It's in unicode, though: fileformat.info/info/unicode/char/226c/index.htm –  Matthew Leingang Nov 1 '10 at 14:15
@Caramdir: Thanks for the edit! (new at this..) –  Alright Nov 1 '10 at 16:48

I found it in the Journal of Combinatorial Optimization (2007) 13:217-221, February 14, 2007: A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. There the expression `\{<,\between\}` has been used, as can be seen in the abstract.

Regarding intervals, `\between` may stand for a crossing/overlapping relation like < for a precedence order and kind of a subset symbol for inclusion/nesting. See also Extracting constrained 2-interval subsets in 2-interval sets.

In such difficult cases, the LaTeX search engine of Springer is a useful tool.

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That's quite a lot of definitions given in a short 5 page paper. @Stefan: how did you actually perform this feat of finding where a symbol is used? –  Willie Wong Nov 1 '10 at 15:35
@Willie: I used Google Code search. –  jnylen Nov 1 '10 at 15:57
That's just great, thanks! And I too would like to know how you found the symbol (which in your case is clearly not with Google Code Search). –  Alright Nov 1 '10 at 16:47
@Alright @Willie: I used the Springer LaTeX search. I will add that to the answer. –  Stefan Kottwitz Nov 1 '10 at 19:34
Once found the relation to intervals, google image search (for interval subsets or 2-intervals) restricted to tiny images immediately gave the other result. Other ways to try in general might be google with options filetype:tex and perhaps additionally site:arxiv.org. –  Stefan Kottwitz Nov 2 '10 at 12:11

It is nor new. It appears on page 28 of "Kummers quartic surface" by R W H T Hudson (Cambridge University Press 1905) without explanation, so was presumably well understood by Projective Geometrists then. Its meaning is still opque to me.

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Further to my last note, it was used by Hudson in "Kummer's Quartic Surface" to denote the inner product of two single-row matrices, for instance (a,b,c,d≬x,y,z,t) = ax+by+cz+dt. The advantage of the notation seems slight and may merely have saved space by not having to write the second matrix as a vertical column in the usual way. –  J F James Nov 24 '12 at 15:03

I have never seen it before so I'm not sure where it comes up. That said, as long as you define your symbols, you can use them for whatever purpose you want. People might be confused if you redefine + as -, but I suspect that `\between` is sufficiently specialized that you can repurpose it as you wish.

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I know. But I usually try to come up with as little new notation as possible. And the name of the symbol is suggestive enough to make me wonder whether other people already have a notation (that symbol) for the same thing. –  Alright Nov 1 '10 at 16:45