Linear Extensions and Comparable Pairs in Partial Orders
Combinatorics
2018-10-16 v3
Abstract
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on elements, which has close to a third of the pairs comparable with high probability: we show that the number of linear extensions is with high probability.
Cite
@article{arxiv.1603.02901,
title = {Linear Extensions and Comparable Pairs in Partial Orders},
author = {Colin McDiarmid and David Penman and Vasileios Iliopoulos},
journal= {arXiv preprint arXiv:1603.02901},
year = {2018}
}
Comments
Authors' accepted manuscript, 20 pages