Level Eulerian Posets

Details Level Eulerian Posets Level Eulerian Posets

2010-09-18

arxiv.org/abs/1009.3585v1

Mathematics

Combinatorics

Scientific paper

The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even order. A condition for verifying shellability is introduced and is automated using the algebra of walks. Applying the Skolem--Mahler--Lech theorem, the ${\bf ab}$-series of a level poset is shown to be a rational generating function in the non-commutative variables ${\bf a}$ and ${\bf b}$. In the case the poset is also Eulerian, the analogous result holds for the ${\bf cd}$-series. Using coalgebraic techniques a method is developed to recognize the ${\bf cd}$-series matrix of a level Eulerian poset.

Affiliated with

Also associated with

No associations

Rating

Level Eulerian Posets 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 Level Eulerian Posets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Level Eulerian Posets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-408476