论文标题
在典范定理的定量方面用于边订单
On quantitative aspects of a canonisation theorem for edge-orderings
论文作者
论文摘要
对于整数，$ k \ ge 2 $和$ n \ ge 2k+1 $有$ k！2^k $ canonical订购的完整$ k $ - 均匀均匀超graph，带有顶点套装$ [n] = \ {1,2，\ dots，\ dots，n \} $。这些正是与任何两个子集$ a，b \ subseteq [n] $相同大小的订购的订购。我们研究了估计的相关构建问题，考虑到$ k $和$ n $，是整数$ n $最少的，因此，无论$ k $ subsets of $ [n] $的订购方式如何，总会存在$ n $ element seet $ x \ subseteq [n] $ k $ k $ k $ subsets oferceed canson上。对于固定的$ k $，我们在这些数字上证明了$ k $乘以$ n $的$ k $ times迭代指数。
For integers $k\ge 2$ and $N\ge 2k+1$ there are $k!2^k$ canonical orderings of the edges of the complete $k$-uniform hypergraph with vertex set $[N] = \{1,2,\dots, N\}$. These are exactly the orderings with the property that any two subsets $A, B\subseteq [N]$ of the same size induce isomorphic suborderings. We study the associated canonisation problem to estimate, given $k$ and $n$, the least integer $N$ such that no matter how the $k$-subsets of $[N]$ are ordered there always exists an $n$-element set $X\subseteq [N]$ whose $k$-subsets are ordered canonically. For fixed $k$ we prove lower and upper bounds on these numbers that are $k$ times iterated exponential in a polynomial of $n$.
