Extremal problems for the Möbius function in the face lattice of the n-octahedron

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13 Scopus citations


We study extremal problems concerning the Möbius function μ of certain families of subsets from On, the lattice of faces of the n-dimensional octahedron. For lower order ideals F from On, |μ(F)| attains a unique maximum by taking F to be the lower two-thirds of the ranks of the poset. Stanley showed that the coefficients of the cd-index for face lattices of convex polytopes are non-negative. We verify an observation that this result implies that the Möbius function is maximized over arbitrary rank-selections from these lattices by taking their odd or even ranks. Using recurrences by Purtill for the cd-index of Bn and On, we demonstrate that the alternating ranks are the only extremal configuration for these two face latties.

Original languageEnglish
Pages (from-to)361-380
Number of pages20
JournalDiscrete Mathematics
Issue number1-3
StatePublished - May 24 1995


  • Convex polytopes
  • Cubical lattice
  • Extremal configuration
  • Lattice of faces
  • Lower order ideals
  • Maximum
  • Möbius function
  • Octahedron
  • Rank selections
  • cd-index

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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