The Lexicographic First Occurrence of a I-II-III pattern

Details The Lexicographic First Occurrence of a I-II-III pattern The Lexicographic First Occurrence of a I-II-III pattern

2008-01-12

arxiv.org/abs/0801.1876v1

Lecture Notes of the London Mathematical Society 376, 213-219, 2010

Mathematics

Probability

Scientific paper

Consider a random permutation $\pi\in{\cal S}_n$. 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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