Acyclic sets of linear orders via the Bruhat orders

@article{Galambos2008AcyclicSO,
title={Acyclic sets of linear orders via the Bruhat orders},
author={{\'A}d{\'a}m Galambos and Victor Reiner},
journal={Social Choice and Welfare},
year={2008},
volume={30},
pages={245-264}
}

We describe Abello’s acyclic sets of linear orders [1] as the permutations visited by commuting equivalence classes of maximal reduced decompositions. This allows us to strengthen Abello’s structural result: we show that acyclic sets arising from this construction are distributive sublattices of the weak Bruhat order. This, in turn, shows that Abello’s acyclic sets are, in fact, the same as Chameni-Nembua’s distributive covering sublattices (S.T.D.C’s). Fishburn’s alternating scheme is shown to… CONTINUE READING