论文标题
关于有序超图的生长功能
On growth functions of ordered hypergraphs
论文作者
论文摘要
对于$ k，l \ ge2 $，我们考虑ed $ l $ l $颜色的理想$ k $ - 均匀的超graphs $（n，χ）$，带有顶点sets $ [n] = \ {1，2，\ dots n \} $，用于$ n \ in \ nathbb {n} $。一个理想是一组这种有色的超图，该图与诱导有序的缩写纸的关系封闭。我们获得了克拉扎尔[Arxiv：0703047]的两个结果的类似物，他们考虑了图，也就是说，我们证明了两种二分法，用于这种有色超图的理想的生长功能。第一个二分法是针对任何$ k，l \ ge2 $的，并说生长功能最终是恒定的，要么至少$ n-k+2 $。 The second dichotomy is only for $k=3,l=2$ and says that the growth function of an ideal of edge two-colored complete $3$-uniform hypergraphs grows either at most polynomially, or for $n\ge23$ at least as $G_n$ where $G_n$ is the sequence defined by $G_1=G_2=1$, $G_3=2$ and $G_n = G_{n-1} + g_ {n-3} $ for $ n \ ge4 $。两个二分法的下限都很紧。
For $k,l\ge2$ we consider ideals of edge $l$-colored complete $k$-uniform hypergraphs $(n,χ)$ with vertex sets $[n]=\{1, 2, \dots n\}$ for $n\in\mathbb{N}$. An ideal is a set of such colored hypergraphs that is closed to the relation of induced ordered subhypergraph. We obtain analogues of two results of Klazar [arXiv:0703047] who considered graphs, namely we prove two dichotomies for growth functions of such ideals of colored hypergraphs. The first dichotomy is for any $k,l\ge2$ and says that the growth function is either eventually constant or at least $n-k+2$. The second dichotomy is only for $k=3,l=2$ and says that the growth function of an ideal of edge two-colored complete $3$-uniform hypergraphs grows either at most polynomially, or for $n\ge23$ at least as $G_n$ where $G_n$ is the sequence defined by $G_1=G_2=1$, $G_3=2$ and $G_n = G_{n-1} + G_{n-3}$ for $n\ge4$. The lower bounds in both dichotomies are tight.
