Notation for the all-ones vector What's the most common way of writing the all-ones vector, that is, the vector, when projected onto each standard basis vector of a given vector space, having length one? The zero vector is frequently written $\vec{0}$, so I'm partial to writing the all-ones vector as $\vec{1}$, but I don't know how popular this is, and I don't know if a reader might confuse it with the identity matrix.
I'm writing for a graph theory audience, if that helps pick a notation.
 A: I use \mathbf{1} in papers (and in books)  In combinatorics it is also common to use $j$, and to use $J$ for the all-ones matrix.  Using $j$ for the all-ones vector has obvious problems since it occurs so often as an index.  No solution is perfect, but I find I have fewer problems with \mathbf{1}.   
I agree you should define it.
Generally I avoid using decorations (tildes, arrows,...) to represent vectors - they look
really ugly on the page.
A: Let $I \subset \{ 1,2,3,\ldots, n \} $. Let $e_I = \sum_{i\in I} e_i.$ Let $[n]=\{ 1,2,3, \ldots, n \} $. 
Then $\vec{1}=e_{[n]}$. Also $e_{\{i\}} = e_i$.
This is not satisfactory to your context, but may have the advantage of alternative usages in subsequent contexts. 
A: Once I had the same problem, I used notation similar to yours: $\mathbf{0}$ for zero-vector and $\mathbf{1}$ for "all-ones vector".


*

*It is NOT common, so you have to define it

*I would not do it unless you have many formulas with it --- if you use it just few times denote it by some letter...
A: I have used the notation $\vec{1}$ in a paper. I think that it's a good choice if you help the reader by defining it.  I did a Google Scholar such of "vector of all ones", and I found a lot of so-so notation such as $e$, $u$, $\mathbf{e}$, $\mathbf{1}$, and even just plain $1$.  I don't think that the literature is loyal to any particular choice.  Confusing $\vec{1}$ with a matrix would be a little strange, because a matrix is suggested by a two-headed arrow, or $\stackrel{\leftrightarrow}{1}$.
A: I like \mathbb'ed ones for this. You can use the mathbbol package by simply saying \mathbb{1}.
A: Clearly there's no consensus on this issue.  Personally, I dislike bold-face anything in papers as it's often hard for the reader to tell whether it's bold-face or not (not everyone has a decent printer + good eyesight).  I would use $\vec{1}$ myself, but it doesn't matter so much, as long as its defined appropriately.
A: I'd say, denote it any way, but please make clear in the introduction that it depends on the basis!
