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Finite Free Resolutions and 1-Skeletons of Simplicial Complexes |
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| Authors: | Naoki Terai Takayuki Hibi |
| Institution: | (1) Department of Mathematics, Faculty of Education, Saga University, Saga 840, Japan;(2) Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka Osaka, 560, Japan |
| Abstract: | A technique of minimal free resolutions of Stanley—Reisner rings enables us to show the following two results: (1) The 1-skeleton of a simplicial (d–1)-sphere is d-connected, which was first proved by Barnette; (2) The comparability graph of a non-planar distributive lattice of rank d–1 is d-connected. |
| Keywords: | simplicial complex 1-skeleton comparability graph d-connected free resolution |
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