# Is there a common symbol for concatenating two (finite) sequences?

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 $\sum (X,Y) = (x_0,...,x_n,y_0,...,y_n)$?

• I have seen more notations for this, the easiest is $XY$.. – Berci Feb 9 '13 at 10:54
• Depending on context, I have seen $XY$, $X\cdot Y$, and $X^{\frown}Y$. – Brian M. Scott Feb 9 '13 at 13:40
• Yes, probably this $X{}^\frown Y$ is the symbol you are looking for. – Berci Feb 9 '13 at 14:03
• I have seen $X||Y$. – Ron Gordon Feb 9 '13 at 14:33
• I've seen lots of notations, but I prefer $X^\frown Y$ because it doesn't seem to be used for anything else. – Andreas Blass Feb 10 '13 at 21:29

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.

• What about concatenation from i=1 to N vectors? – Pedro77 Apr 6 '18 at 22:02
• @Pedro77 How about $\big\Vert_{i=1}^N v_i = v_1 \Vert \dots \Vert v_N$? – user76284 Jul 19 '18 at 21:13

The same question on Tex SE.

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.)

• 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. – Warbo Dec 7 '15 at 10:20
• Wouldn't $X\times Y$ be the Cartesian Product of $X$ and $Y$? – Mr Pie Dec 26 '17 at 4:14

$\newcommand\mdoubleplus{\mathbin{+\mkern-10mu+}}$ In haskell the $\mdoubleplus$ operator is used for concatenating lists.

You can define it in latex using the command

\newcommand\mdoubleplus{\mathbin{+\mkern-10mu+}}

• You'd have to pay your secretary a lot more to type all that for one symbol. :) – DanielWainfleet Aug 5 '16 at 13:06
• @user254665 That would be written once, at the top of the document, and thereafter \mdoubleplus can be used. – OJFord Feb 24 '17 at 14:01

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 $xy$.

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, $X+\!\!+Y$.

• i didn't know about \!. thanks\!! – anthonybell Feb 9 '17 at 0:12