Compression with wildcards: abstract simplicial complexes

Despite the more handy terminology of abstract simplicial complexes , in its core this article is about antitone Boolean functions. Given maximal faces (=facets) our main algorithm, called Facets-To-Faces, outputs a compressed format. The degree compression which programmed using high-level programming language Mathematica, compares favorably to both hardwired Mathematica command BooleanConvert, and binary decision diagrams provided by Python. A novel way calculate face-numbers from facets also presented. Both algorithms can be parallelized are applicable (e.g.) reliability analysis, combinatorial topology, frequent-set-mining.