On-line chain partitioning problem of on-line posets has been open for the past 20 years. The best known on-line algorithm uses 5w −1 4 chains to cover poset of width w. Felsner ...
The posets of dimension 2 are those posets whose minimal realizations have two elements, that is, which may be obtained as the intersection of two of their linear extensions. Gall...
Given a poset P = (X, ), a partition X1, . . . , Xk of X is called an ordered partition of P if, whenever x Xi and y Xj with x y, then i j. In this paper, we show that for ever...
We prove analogues for sub-posets of the Dowling lattices of the results of Calderbank, Hanlon, and Robinson on homology of sub-posets of the partition lattices. The technical too...