[Feature request] Spider set space, cardinality and its complement

[brunolnetto]

Description

Statement : spider sets are possible disjoint union sets of exclusive sets on Euler sets
Example: Given sets A and B as well as non-empty intersection set AB, we call the spider-set space {S} as a list of lists:

[ [A], [B], [AB], [A, B], [A, AB], [AB, B], [A, B, AB] ]

Cardinality: A Venn-set with n sets may have 2^n-1 exclusive sets, but it is oftentimes much lower than it i.e. m << 2^n-1. Therefore, the spider-set space cardinality s is equal to the sum of sets cardinality from 1 to m i.e. 2^m-1.

Complement: Additionally, let us define a spider set-element S e.g. its complement R-set is such that R + S gives the non-empty universe Euler set E, with m-cardinality. It means, R-set is given by the difference E - S of Euler E-set by S-set.

Implementation: spider_sets(sets, k)

1. Implement euler sets keys;
2. Find a rationale to allow a brief spider description throughout its k <= m leg-landing sets. The cardinality of such subset of sets is k!/(m! (m-k)!). The greatest cardinality occurs for equality k=ceil(m/2)

References

Layman's: https://en.wikipedia.org/wiki/Spider_diagram
Academic: https://www.cs.kent.ac.uk/pubs/2006/2972/content.pdf