How to partition or count an abstract simplicial complex, given its facets
Abstract
Given are the facets of an abstract (finite) simplicial complex SC. We show how to partition SC into few pieces, each one compactly encoded by the use of wildcards. Such a representation is useful for the optimization of a target function SC -> Z, as well as in combinatorial commutative algebra and Frequent Set Mining. Merely calculating the face-numbers of SC can be done faster than partitioning SC. Our method compares favorably to inclusion-exclusion and binary decision diagram
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.