Title: An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likes,
Abstract: Achieving the goals in the title (and others) relies on a cardinality-wise
scanning of the ideals of the poset. Specifically, the relevant numbers
attached to the k+1 element ideals are inferred from the corresponding numbers
of the k-element (order) ideals. Crucial in all of this is a compressed
representation (using wildcards) of the ideal lattice. The whole scheme invites
distributed computation.