论文标题
高度邻居中心对称球的新家庭
New families of highly neighborly centrally symmetric spheres
论文作者
论文摘要
1995年，Josckusch建造了一个无限的中央对称家族（CS，简称为简短的三角剖分），其3 $ -SPHERES的CS- $ 2 $ -2 $ -NEIGHBORLY。最近，Novik和Zheng扩展了Jockusch的建筑：对于所有$ d $和$ n> d $，他们构建了$ d $ -sphere的CS三角测量，带有$ 2N $ Vertices，$Δ^d_n $，即CS-$ \ lceil d/2 \ lceil d/2 \ rceil $ -neigh-neigh $ - neigh-neigh $。在这里，提供了几种与$δ^d_n $有关的新CS构造。结果表明，对于所有$ k> 2 $和一个足够大的$ n $，还有另一个CS三角剖分（2k-1）$ - 带有$ 2N $的顶点的cs- $ k $ neighborly，而对于$ k = 2 $，则$ω（2^n）$ pairwise y pairwise dopywise nonwise nonwise nonwise nonwise nonwise nocywise nor-Isomorphic triangulations。还表明，对于所有$ k> 2 $和一个足够大的$ n $，有$ω（2^n）$成对的非同构CS CS三角形的$（2K-1）$ - 带有$ 2N $的顶点的$ 2N $ VERTICES，是CS-$（$（K-1）$ - 邻居。这些结构基于研究$δ^d_n $的方面，尤其是在某些必要的和一些足够的条件下，精神与大风的均匀条件相似。一路上证明，Jockusch的Spheres $δ^3_n $是可撒的，对Murai的肯定答案 - 尼沃关于$ 2 $的可壳可壳的问题。
In 1995, Josckusch constructed an infinite family of centrally symmetric (cs, for short) triangulations of $3$-spheres that are cs-$2$-neighborly. Recently, Novik and Zheng extended Jockusch's construction: for all $d$ and $n>d$, they constructed a cs triangulation of a $d$-sphere with $2n$ vertices, $Δ^d_n$, that is cs-$\lceil d/2\rceil$-neighborly. Here, several new cs constructions, related to $Δ^d_n$, are provided. It is shown that for all $k>2$ and a sufficiently large $n$, there is another cs triangulation of a $(2k-1)$-sphere with $2n$ vertices that is cs-$k$-neighborly, while for $k=2$ there are $Ω(2^n)$ such pairwise non-isomorphic triangulations. It is also shown that for all $k>2$ and a sufficiently large $n$, there are $Ω(2^n)$ pairwise non-isomorphic cs triangulations of a $(2k-1)$-sphere with $2n$ vertices that are cs-$(k-1)$-neighborly. The constructions are based on studying facets of $Δ^d_n$, and, in particular, on some necessary and some sufficient conditions similar in spirit to Gale's evenness condition. Along the way, it is proved that Jockusch's spheres $Δ^3_n$ are shellable and an affirmative answer to Murai--Nevo's question about $2$-stacked shellable balls is given.
