Refreshing the memory : Notations

Question

Can anyone please tell me what does the 1n1, 1n2 mean ?

Is it a one-hot vector of size n1, n2 or it's just a random vector of that size ?

Thank you

Answer 1

It is a vector of all ones, of size $n_1 \times 1$ or $n_2 \times 1$. In summation notation, the two constraints are \begin{align} \sum_{j=1}^{n_2} X_{i,j} &= 1 &&\text{for $i\in\{1,\dots,n_1\}$} \\ \sum_{i=1}^{n_1} X_{i,j} &\le 1 &&\text{for $j\in\{1,\dots,n_2\}$} \end{align}