Say we have two finite sequences $X = (x_0,...,x_n)$ and $Y = (y_0,...,y_n)$. Is there a more or less common notation for the concatenation of these sequences, like $\sum (X,Y) = (x_0,...,x_n,y_0,...,y_n)$?
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asked Feb 9 '13 at 10:42
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2$\begingroup$ I have seen more notations for this, the easiest is $XY$.. $\endgroup$ – Berci Feb 9 '13 at 10:54
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5$\begingroup$ Depending on context, I have seen $XY$, $X\cdot Y$, and $X^{\frown}Y$. $\endgroup$ – Brian M. Scott Feb 9 '13 at 13:40
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1$\begingroup$ Yes, probably this $X{}^\frown Y$ is the symbol you are looking for. $\endgroup$ – Berci Feb 9 '13 at 14:03
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4$\begingroup$ I have seen $X||Y$. $\endgroup$ – Ron Gordon Feb 9 '13 at 14:33
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2$\begingroup$ I've seen lots of notations, but I prefer $X^\frown Y$ because it doesn't seem to be used for anything else. $\endgroup$ – Andreas Blass Feb 10 '13 at 21:29
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The comments suggest the following notations for the concatenation of $X$ and $Y$:
- $X^\frown Y$ (given by
X^\frown Y); - $XY$ (given by
XY); - $X \cdot Y$ (given by
X \cdot Y); - $X \mathbin\Vert Y$ (given by
X \mathbin\Vert Y);
of which the first seems not to be in use for other concepts, making it especially suitable.
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From there, and more:
- $X \oplus Y$ (given by
X \oplus Y); - $(X,Y)$ (given by
(X,Y));
I would avoid $X \times Y$, $XY$ or $X \cdot Y$ to not confuse it with any sort of multiplication / product.
And I would also not use $X \otimes Y$ because it is usually the tensor product. (See also here.)
Some relevant Wikipedia pages with common notations:
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2$\begingroup$ I would avoid
(X, Y)for concatenation, as it conflicts with the notation used for sequences(x_0, ..., x_n); appearing to be a sequence containing two sequences. $\endgroup$ – Warbo Dec 7 '15 at 10:20 -
$\begingroup$ Wouldn't $X\times Y$ be the Cartesian Product of $X$ and $Y$? $\endgroup$ – Mr Pie Dec 26 '17 at 4:14
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$\newcommand\mdoubleplus{\mathbin{+\mkern-10mu+}}$ In haskell the $ \mdoubleplus $ operator is used for concatenating lists.
You can define it in latex using the command
\newcommand\mdoubleplus{\mathbin{+\mkern-10mu+}}
answered Feb 18 '15 at 12:12
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1$\begingroup$ You'd have to pay your secretary a lot more to type all that for one symbol. :) $\endgroup$ – DanielWainfleet Aug 5 '16 at 13:06
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2$\begingroup$ @user254665 That would be written once, at the top of the document, and thereafter
\mdoublepluscan be used. $\endgroup$ – OJFord Feb 24 '17 at 14:01
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If $x$ and $y$ are finite sequences, you could denote their concatenation by $xy$. Let me explain. There's at least two ways of formalizing the statement "$x$ and $y$ are finite sequences in $X$"
$x$ and $y$ are functions of type $[\:\!n) \rightarrow X$, where $[\:\!n)$ is a shorthand for the set $\{0,\ldots,n-1\}$.
$x$ and $y$ are elements of $X^*$, where $X^*$ is the monoid freely generated by $X$.
If you're interested in concatenating these things, then you should probably take the second perspective, in which case the concatenation of $x$ and $y$ is simply their product in the monoid $X^*$, which is denoted $xy$.
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In formal specifications, one way to concatenate two sequences is using the Haskell concatenation symbol as indicated in one of the comments above. In a tex editor one can type the following: X +\!\!+ Y. The result appears like this, $X+\!\!+Y$.
