I-II-III模式的词典学首次出现
The Lexicographic First Occurrence of a I-II-III pattern
摘要：
考虑随机置换$π\in{\cal S}_n$。在本文中，也许最好归类为离散概率分布理论的贡献，我们研究了{ \it第一}出现$X=X_n$的I-II-III模式，其中“第一”是解释的字典顺序诱导的3个子集的$[n]=\{1,2,...,n\}$。当然，如果置换是I-II-III-避免的，那么第一个I-II-III-模式永远不会出现，因此每个$n$的$\e(X)=\infty$;为了避免这种情况，我们还研究了给定双射$f:{\bf Z}^+\to{\bf Z}^+$的I-II-III-模式的第一次出现。
英文摘要：
Consider a random permutation $π\in{\cal S}_n$. In this paper, perhaps best classified as a contribution to discrete probability distribution theory, we study the {\it first} occurrence $X=X_n$ of a I-II-III-pattern, where "first" is interpreted in the lexicographic order induced by the 3-subsets of $[n]=\{1,2,...,n\}$. Of course if the permutation is I-II-III-avoiding then the first I-II-III-pattern never occurs, and thus $\e(X)=\infty$ for each $n$; to avoid this case, we also study the first occurrence of a I-II-III-pattern given a bijection $f:{\bf Z}^+\to{\bf Z}^+$.
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