Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals

Details Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals

2005-02-17

arxiv.org/abs/math/0502386v3

Mathematics

Combinatorics

23 pp, considerable revision

Scientific paper

We introduce two polynomials (in $q$) associated with a finite poset $P$ that encode some information on the covering relation in $P$. If $P$ is a distributive lattice, and hence $P$ is isomorphic to the poset of dual order ideals in a poset $L$, then these polynomials coincide and the coefficient of $q$ equals the number of $k$-element antichains in $L$. In general, these two covering polynomials are different, and we introduce a deviation polynomial of $P$, which measures the difference between these two. We then compute all these polynomials in the case, where $P$ is one of the posets associated with an irreducible root system. These are 1) the posets of positive roots, 2) the poset of ad-nilpotent ideals, and 3) the poset of Abelian ideals.

Affiliated with

Also associated with

No associations

Rating

Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-97506