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Order Quasisymmetric Functions Distinguish Rooted Trees
Richard P. Stanley conjectured that finite trees can be distinguished by
their chromatic symmetric functions. In this paper, we prove an analogous
statement for posets: Finite rooted trees can be distinguished by their order
quasisymmetric functions.Comment: 16 pages, 5 figures, referees' suggestions incorporate
A note on blockers in posets
The blocker of an antichain in a finite poset is the set of
elements minimal with the property of having with each member of a common
predecessor. The following is done:
1. The posets for which for all antichains are characterized.
2. The blocker of a symmetric antichain in the partition lattice is
characterized.
3. Connections with the question of finding minimal size blocking sets for
certain set families are discussed
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