Notation for building ordered sets of zeros I want to define a lattice where each site is occupied by an ordered set of zeros. Later in the calculation, the zeros grow to nonnegative integers, but I need to start with zeros.  At the $i$th site, there should be $n_i$ zeros.  The set of zeros at the $i$th site is denoted $x_i$.  What is a nice way of denoting the set at the $i$th site?
$x_i =   ( j_k = 0   \;|\: k \in \mathbb{N} , k \le n_i)$
or
$x_i =   ( 0   \;|\: k \in \mathbb{N} , k \le n_i).$
The top expression with $j_k$ seems excessively complicated, but I don't think the bottom expression is allowed?

How about simply
$$ x_i = (\underbrace{0,0,\ldots,0}_{n_i\text{ zeros}}) $$
That's the most readable way to write it, and should therefore be preferred unless you have to placate someone who has harsh views on what is and isn't allowed in mathematical writing.
Second best, I think, would be something like
$$ x_i = (0)_{j\in\{1,2,\ldots, n_i\}} $$
If anything involving "$\ldots$" is disallowed, you'd have to write
$$ x_i = (0)_{1\le j\le n_i} $$
but then human readability begins to really suffer because it's not immediately clear that $j$ is meant to be an index variable.
