Download

To support experiments with our catalogue, we provide all permutational types of indecomposable min-semi-balanced set systems for \(N = 3,4,5,6\) available to download in CSV (comma separated values) files.

File format

In this case, we assume \(N\) to be a subset of letters, that is, in case of \(|N| = 3\) take \(N = \{a,b,c\}\).

The format of the file is the following:

The first line of the file contains a header. The header contains all subsets of \(N\). We encode set \(\{a,b\}\) as a string \(ab\). In the case of \(|N| = 3\), the header is the following, where the empty string at the beginning of the line stands for \(\emptyset\):
```
"";"a";"b";"c";"ab";"ac";"bc";"abc"
```
Each other line contains one coefficient vector \(\theta\) (after moving all terms on the right hand side). More specifically, one has \(\theta (S)= -\lambda_{S}\) for \(S\in\mathcal{S}\), \(\theta(N)=r\), \(\theta (\emptyset)= 1-r\), and \(\theta (L)=0\) other \(L\subseteq N\), where \(\sum_{S\in\mathcal{S}} \lambda_{S}\cdot\chi_{S}\) is the corresponding non-zero semi-conic combination with integer coefficients \(\lambda_{S}\) yielding a constant vector in \(\mathbb{R}^{N}\) with shared component \(r\). For example, one can take \(\mathcal{S}:=\{a,b,ab\}\) in which case the corresponding semi-conic combination is \[1\cdot\chi_{a}+1\cdot\chi_{b}+(-1)\cdot\chi_{ab}\] is zero vector in \(\mathbb{R}^{N}\), which means \(r=0\). This gives \(\theta(\emptyset)=1\), \(\theta(a)=\theta(b)=-1\), \(\theta(ab)=1\) and \(\theta(L)=0\) otherwise. In case \(|N|=3\) this is a representative of the only permutational type in the first classification class represented by the next line.
```
1;-1;-1;0;1;0;0;0
```