Finite Free Resolutions and 1-Skeletonsof Simplicial Complexes

  • Authors:

  • Naoki Terai;Takayuki Hibi

  • Affiliations:

  • Department of Mathematics, Faculty of Education, Saga University, Saga 840, Japan E-mail: terai@cc.saga-u.ac.jp;Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka Osaka 560, Japan E-mail: hibi@math.sci.osaka-u.ac.jp

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 1997

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Abstract

A technique of minimal free resolutions of Stanley--Reisner rings enables us to show the following two results: (1) The 1-skeletonof a simplicial (d-1)-sphere is d-connected, which was firstproved by Barnette; (2) The comparability graph of a non-planar distributive lattice of rank d-1 is d-connected.