论文标题
中央对称复合物和下限定理的应力
The stresses on centrally symmetric complexes and the lower bound theorems
论文作者
论文摘要
1987年，史丹利（Stanley）猜想，如果中央对称的cohen--macaulay simpericial simpericial complect $ dimension $ d-1 $的$ d-1 $满足$ h_i（δ）= \ binom {d} {i} {i} $ for Some $ i \ geQ 1 $，然后最近，Klee，Nevo，Novik和Zheng猜想，如果中央对称的简单polytope $ p $ dimension $ d $的$ d $满足$ g_i（\ partial p）= \ binom {d} {d} {i} {i} {i} - \ binom {d} $ gee pe 1 q e qe {i-d} $ deq $ deq $ d y q \ q ge q y q eq $ d iq $ g_j（\ partial p）= \ binom {d} {j} - \ binom {d} {d} {j-1} $ for ALL $ d/2 \ geq j \ geq i $。本说明使用应力空间来证明这两个猜想。
In 1987, Stanley conjectured that if a centrally symmetric Cohen--Macaulay simplicial complex $Δ$ of dimension $d-1$ satisfies $h_i(Δ)=\binom{d}{i}$ for some $i\geq 1$, then $h_j(Δ)=\binom{d}{j}$ for all $j\geq i$. Much more recently, Klee, Nevo, Novik, and Zheng conjectured that if a centrally symmetric simplicial polytope $P$ of dimension $d$ satisfies $g_i(\partial P)=\binom{d}{i}-\binom{d}{i-1}$ for some $d/2\geq i\geq 1$, then $g_j(\partial P)=\binom{d}{j}-\binom{d}{j-1}$ for all $d/2\geq j\geq i$. This note uses stress spaces to prove both of these conjectures.
