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arXiv · 1704.07708

An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likes

Marcel Wild
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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.

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Marcel Wild. 2017-04-25. An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likes. https://arxiv.org/abs/1704.07708

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