论文标题
在$ r $ $ - 万甲基细分的$ f $ - 向量上
On the $f$-vectors of $r$-multichain subdivisions
论文作者
论文摘要
对于POSET $ P $和整数$ r \ geq 1 $，让$ p_r $是$ p $中所有$ r $ $ ultichains的集合。对应于每个严格增加地图$ı：[r] \ rightarrow [2r] $，$ p_r $上的订单$ \preceq_ı$。令$ \ d（g_ı（p_r））$是图形$g_ı$与$ p_r $和$ $ $相关的集团综合体。在最近的论文\ cite {nw}中，显示出$ \ d（g_ı（p_r））$是一类严格增加地图的$ p $的细分。在本文中，我们表明所有这些细分都具有相同的$ f $ - 向量。当$ f $ $ f $ $ f $的转换矩阵和$ f $ - $ f $ - 和$ h $ - $ h $ - - 当$ p $是$ p $的面孔的面孔$ \ d $时，我们将$ f $ $δ$的变换矩阵的明确说明。我们研究了两个重要的细分，Cheeger-Müller-Schrader的细分和$ r $颜色的Barycentric细分，属于我们的$ r $ $ -Multichain细分。
For a poset $P$ and an integer $r\geq 1$, let $P_r$ be a collection of all $r$-multichains in $P$. Corresponding to each strictly increasing map $ı:[r]\rightarrow [2r]$, there is an order $\preceq_ı$ on $P_r$. Let $\D(G_ı(P_r))$ be the clique complex of the graph $G_ı$ associated to $P_r$ and $ı$. In a recent paper \cite{NW}, it is shown that $\D(G_ı(P_r))$ is a subdivision of $P$ for a class of strictly increasing maps. In this paper, we show that all these subdivisions have the same $f$-vector. We give an explicit description of the transformation matrices from the $f$- and $h$-vectors of $Δ$ to the $f$- and $h$-vectors of these subdivisions when $P$ is a poset of faces of $\D$. We study two important subdivisions Cheeger-Müller-Schrader's subdivision and the $r$-colored barycentric subdivision which fall in our class of $r$-multichain subdivisions.
