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A characterization of simplicial polytopes with g_2 = 1 | Eran Nevo
; Eyal Novinsky
; | Date: |
11 Apr 2008 | Abstract: | Kalai proved that the simplicial polytopes with g_2=0 are the stacked
polytopes. We characterize the g_2=1 case. Specifically, we prove that every
simplicial d-polytope (d>3) which is prime and with g_2=1 is combinatorially
equivalent either to a join of two simplices whose dimensions add up to d (each
of dimension at least 2), or to a join of a polygon with a (d-2)-simplex. Thus,
every simplicial d-polytope (d>3) with g_2=1 is combinatorially equivalent to a
polytope obtained by stacking over a polytope as above. Moreover, the above
characterization holds for any homology (d-1)-sphere (d>3) with g_2=1. | Source: | arXiv, 0804.1813 | Services: | Forum | Review | PDF | Favorites |
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