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math.CO2005
The poset of positive roots and its relatives
Dmitri I. Panyushev
Let be a root system with a subset of positive roots, . We consider edges of the Hasse diagrams of some posets associated with . For each edge one naturally defines i…
math.CO2005
Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals
Dmitri I. Panyushev
We introduce two polynomials (in ) associated with a finite poset that encode some information on the covering relation in . If is a distributive lattice, and hence $…