Squarefree P-modules and the cd-index

Satoshi Murai*, Kohji Yanagawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper, we introduce a new algebraic concept, which we call squarefree P-modules. This concept is inspired from Karu's proof of the non-negativity of the cd-indices of Gorenstein* posets, and supplies a way to study cd-indices from the viewpoint of commutative algebra. Indeed, by using the theory of squarefree P-modules, we give several new algebraic and combinatorial results on CW-posets. First, we define an analogue of the cd-index for any CW-poset and prove its non-negativity when a CW-poset is Cohen-Macaulay. This result proves that the h-vector of the barycentric subdivision of a Cohen-Macaulay regular CW-complex is unimodal. Second, we prove that the Stanley-Reisner ring of the barycentric subdivision of an odd dimensional Cohen-Macaulay polyhedral complex has the weak Lefschetz property. Third, we obtain sharp upper bounds of the cd-indices of Gorenstein* posets for a fixed rank generating function.

Original languageEnglish
Pages (from-to)241-279
Number of pages39
JournalAdvances in Mathematics
Publication statusPublished - 2014 Nov 10
Externally publishedYes


  • Barycentric subdivisions
  • Cd-Index
  • Flag f-vectors
  • Regular CW-complexes
  • Stanley-Reisner rings

ASJC Scopus subject areas

  • Mathematics(all)


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