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- W2889366973 abstract "Let $mu_{text{2n}}(d,v)$ (respectively, $mu^{text{s}}_{text{2n}}(d,v)$) be the minimal number of facets of a (simplicial) 2-neighborly $d$-polytope with $v$ vertices, $v > d ge 4$. It is known that $mu_{text{2n}}(4,v) = v (v-3)/2$, $mu_{text{2n}}(d, d+2) = d+5$, $mu_{text{2n}}(d,d+3) = d+7$ for $d ge 5$, and $mu_{text{2n}}(d,d+4) in [d+5, d+8]$ for $d ge 6$. We show that $mu_{text{2n}}(5, v) = Omega(v^{4/3})$, $mu_{text{2n}}(6, v) ge v$, and the equality $mu_{text{2n}}(6, v) = v$ holds only for a simplex and for a dual 2-neighborly 6-polytope (if it exists) with $v ge 27$. By using $g$-theorem, we get $mu^{text{s}}_{text{2n}}(d, v) = Delta (Delta(d-3) + 3d - 5)/2 + d + 1$, where $Delta = v - d - 1$. Also we show that $mu_{text{2n}}(d, v) ge d+7$ for $v ge d+4$." @default.
- W2889366973 created "2018-09-07" @default.
- W2889366973 creator A5042813130 @default.
- W2889366973 date "2018-08-29" @default.
- W2889366973 modified "2023-09-27" @default.
- W2889366973 title "On the minimum number of facets of a 2-neighborly polytope" @default.
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