Omnibus Sequences, Coupon Collection, and Missing Word Counts

被引：6

作者：

Abraham, Sunil ^{[1
]}

Brockman, Greg ^{[2
]}

Sapp, Stephanie ^{[3
]}

Godbole, Anant P. ^{[4
]}

机构：

[1] Univ Oxford, Oxford, England

[2] MIT, Cambridge, MA 02139 USA

[3] Univ Calif Berkeley, Berkeley, CA 94720 USA

[4] E Tennessee State Univ, Johnson City, TN 37614 USA

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2013年 / 15卷 / 02期

基金：

美国国家科学基金会;

关键词：

Coupon collection; Omnibus sequences; Extreme value distribution;

D O I：

10.1007/s11009-011-9247-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we study the properties of k-omnisequences of length n, defined to be strings of length n that contain all strings of smaller length k embedded as (not necessarily contiguous) subsequences. We start by proving an elementary result that relates our problem to the classical coupon collector problem. After a short survey of relevant results in coupon collection, we focus our attention on the number M of strings (or words) of length k that are not found as subsequences of an n string, showing that there is a gap between the probability threshold for the emergence of an omnisequence and the zero-infinity threshold for .

引用

页码：363 / 378

页数：16

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