日本語
 
User Manual Privacy Policy ポリシー/免責事項 連絡先
  詳細検索ブラウズ

アイテム詳細


公開

学術論文

On the distribution of the number of missing words in Random texts

MPS-Authors
/persons/resource/persons50480

Rahmann,  Sven
Dept. of Computational Molecular Biology (Head: Martin Vingron), Max Planck Institute for Molecular Genetics, Max Planck Society;

URL
There are no locators available
フルテキスト (公開)
公開されているフルテキストはありません
付随資料 (公開)
There is no public supplementary material available
引用

Rahmann, S. (2003). On the distribution of the number of missing words in Random texts. Combinatorics, Probability and Computing, 12(1), 72-87. doi:10.1017/S0963548302005473.


引用: http://hdl.handle.net/11858/00-001M-0000-0010-8B01-6
要旨
Determining the distribution of the number of empty urns after a number of balls have been thrown randomly into the urns is a classical and well understood problem. We study a generalization: Given a finite alphabet of size [sigma] and a word length q, what is the distribution of the number X of words (of length q) that do not occur in a random text of length n+q[minus sign]1 over the given alphabet? For q=1, X is the number Y of empty urns with [sigma] urns and n balls. For q[gt-or-equal, slanted]2, X is related to the number Y of empty urns with [sigma]q urns and n balls, but the law of X is more complicated because successive words in the text overlap. We show that, perhaps surprisingly, the laws of X and Y are not as different as one might expect, but some problems remain currently open.