Level Eulerian Posets

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2 Scopus citations


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 ab-series of a level poset is shown to be a rational generating function in the non-commutative variables a and b. In the case the poset is also Eulerian, the analogous result holds for the cd-series. Using coalgebraic techniques a method is developed to recognize the cd-series matrix of a level Eulerian poset.

Original languageEnglish
Pages (from-to)857-882
Number of pages26
JournalGraphs and Combinatorics
Issue number4
StatePublished - Jul 2013


  • Eulerian posets
  • Infinite voltage graph
  • Rational generating function
  • Shelling
  • Spheres
  • cd-index and cd-series

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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