Einstein notation $-$ or another $-$ to denote constraints in high dimensional ILP problems When discussing marginal sums of arrays in 3 dimensions or more, is it customary in the statistical and/or data science communities to use the Einstein summation convention? Is some other form preferred?
The context is an integer linear programming (ILP) optimization problem where the decision variables are $X\in\mathbb{R}^{I \times J \times K}$ and $z \in \mathbb{R}^I$, and the constraints involve marginal sums on $X$. Should I (may I?) use
$$
\begin{matrix}
\min ~~~ &C^{ijk}X_{ijk} + \tau^i z_i & \\
\text{s.t.}  &1^{ijk} X_{ijk} &= 10 \\
& 1^kX_{ijk} 1_j &\preccurlyeq 10z \\
& 1^{ik}X_{ijk} &\succcurlyeq \bf{1}_J
\end{matrix}
$$
Is there some other "standard" way to say this? I'm trying to avoid $\sum_{ijk}X_{ijk}=10$ as I am writing a spec for software that eschews loops and summations in factor of matrix and inner products.
I am just looking for a generally-accepted notation for inner product-like constructs/marginalizations for higher dimensional arrays.

Follow-up: It is perhaps obvious that any 3-dimensional-or-higher array (3rd order tensor or higher) can be serialized into a regular 2D array (by concatenating the 2nd and all subsequent layers/levels of the array on to the side or bottom of the top layer/level), so for all practical purposes, e.g., writing technical specifications, the 2D matrix notation is sufficient.

In my experience, the Einstein convention is rarely used in statistics and machine learning, although NumPy functions like numpy.einsum are there to help you with this.
In many cases, an index-free version is preferred, something well-known in math and physics, too. E.g., scalar products are not written as $\sum_i x_iy_i$ but rather as $\langle \mathbf x, \mathbf y\rangle$, or the trace is rather $\operatorname tr(M)$ than $\sum_i M_{ii}$.
And if there is some contraction that you don't know an established coordinate-free notation for, maybe you define a new operator yourself.
As with math and physics, the best solution, if possible, would be to use notation that is independent of the coordinate basis (or the coordinate chart if you use non-linear spaces).
(I wrote "best solution", but this is rather subjective. There are highly respected scientists that clearly prefer the coordinate notation.)
