Definitions
Define a vector Tuples[a[0, 1], n]
of elements $a[i_1,...,i_n], i_j \in \{0,1\} ~\forall j$, that is for instance
{a[0, 0, 0, 0], a[0, 0, 0, 1], a[0, 0, 1, 0], a[0, 0, 1, 1], a[0, 1, 0, 0], a[0, 1, 0, 1], a[0, 1, 1, 0], a[0, 1, 1, 1], a[1, 0, 0, 0], a[1, 0, 0, 1], a[1, 0, 1, 0], a[1, 0, 1, 1], a[1, 1, 0, 0], a[1, 1, 0, 1], a[1, 1, 1, 0], a[1, 1, 1, 1]}
with n=4,
Define a set of tuples $I_{l_k}\in \mathbb{R}^l$ with $l\in \{1,...,n-1\}$ and $k\in \{1,...,\binom{l}{n}\}$. For instance with n=2, there is one possible value for $l$, that is $l=1$. Therefore, there exist 2 different tuple $I_{1_1}=\{1\}$ and $I_{1_2}=\{2\}$. For n=3, there is two possible value for $l$, that is $l=1$ and $l=2$. Therefore, for $l=1$ there exists 3 different tuple $I_{1_1}=\{1\}$, $I_{1_2}=\{2\}$ and $I_{1_3}=\{3\}$. For $l=2$, there exists 3 different tuple $I_{2_1}=\{1,2\}$, $I_{2_2}=\{1,3\}$ and $I_{3_3}=\{2,3\}$.
Goal
I would like to generate a matrix $M_{I_{l_k}}$ whose elements are the elements of the vector Tuples[a[0, 1], n]
, with respect to a given tuple $I_{l_k}$ in the following way :
The rows are the elements of Tuples[a[0, 1], n]
whose indices $i_j$ whose location $j$ is specified by the elements of the tuple $I_{l_k}$ are constant while the other indices vary from 0 to 1 in a binary order. The column are the elements of Tuples[a[0, 1], n]
whose indices $i_j$ whose location $j$ is not specified by the elements of the tuple $I_{l_k}$ are constant while the other indices vary from 0 to 1 in a binary order.
Example
Here is the example for n=3. Since I can't write it in LaTeX here for some unknown reasons, this is a printscreen from a document.
I
, and I think it's because I don't understandk
. Isk
a member of the setRange[Binominal[n-1,n]]
? $\endgroup$