An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likes
Data Structures and Algorithms
2017-04-26 v1
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.
Cite
@article{arxiv.1704.07708,
title = {An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likes},
author = {Marcel Wild},
journal= {arXiv preprint arXiv:1704.07708},
year = {2017}
}
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nine pages