论文标题
完成和扩展顶点分解复合物的炮击
Completing and extending shellings of vertex decomposable complexes
论文作者
论文摘要
我们说，如果$ n $ dertices上的纯$ d $ d $ d $ d $ d $δ$是\ emph {bleassing completable}，如果$δ$可以实现为$Δ_{n-1}^{n-1}^{（d）} $的初始序列，$ d $ d $ - d $ - d $ - skeleton of $ d $（n-n-1）西蒙（Simon）的一个众所周知的猜想认为，任何可壳的复合物都可以完成。在本说明中，我们证明顶点可分解的复合物是可以完成的。实际上，我们表明，如果$δ$是一个顶点可分解的复合体，则存在其接地套件$ v $的订购，从而添加最小的丢失$（d+1）$ - $ v $的子集$ v $的子集在一个复杂的复合体中又是vertex decomposoposcomble。我们探索了针对矩形和转移复合物的应用程序，以及与山脊 - 串联复合物和$ k $ - 兼容性的连接。我们还表明，如果$δ$是$ d $二维复合体，最多是$ d+3 $顶点，那么可撒，可分解的概念，可分解的，可完全的壳和可撒的概念都是等效的。
We say that a pure $d$-dimensional simplicial complex $Δ$ on $n$ vertices is \emph{shelling completable} if $Δ$ can be realized as the initial sequence of some shelling of $Δ_{n-1}^{(d)}$, the $d$-skeleton of the $(n-1)$-dimensional simplex. A well-known conjecture of Simon posits that any shellable complex is shelling completable. In this note we prove that vertex decomposable complexes are shelling completable. In fact we show that if $Δ$ is a vertex decomposable complex then there exists an ordering of its ground set $V$ such that adding the revlex smallest missing $(d+1)$-subset of $V$ results in a complex that is again vertex decomposable. We explore applications to matroids and shifted complexes, as well as connections to ridge-chordal complexes and $k$-decomposability. We also show that if $Δ$ is a $d$-dimensional complex on at most $d+3$ vertices then the notions of shellable, vertex decomposable, shelling completable, and extendably shellable are all equivalent.
