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Rigidity and the Lower Bound Theorem for Doubly Cohen-Macaulay Complexes | | Eran Nevo
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16 May 2005 | | Subject: | Combinatorics MSC-class: 52C25; 13F55 | math.CO | | Abstract: | We prove that for $dgeq 3$, the 1-skeleton of any $(d-1)$-dimensional doubly Cohen Macaulay (abbreviated 2-CM) complex is generically $d$-rigid. This implies the following two corollaries (by Kalai and Lee respectively): Barnette’s lower bound inequalities for boundary complexes of simplicial polytopes hold for every 2-CM complex (of dimension $geq 2$). Moreover, the initial part $(g_0,g_1,g_2)$ of the $g$-vector of a 2-CM complex (of dimension $geq 3$) is an $M$-sequence. It was conjectured by Björner and Swartz that the entire $g$-vector of a 2-CM complex is an $M$-sequence. | | Source: | arXiv, math.CO/0505334 | | Services: | Forum | Review | PDF | Favorites | |
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