✦ LIBER ✦

The statistics of words on rings

✍ Scribed by Jerome K. Percus; Ora E. Percus

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 125 KB
Volume: 59
Category: Article
ISSN: 0010-3640
DOI: 10.1002/cpa.20096

No coin nor oath required. For personal study only.

✦ Synopsis

We analyze sequences of letters on a ring. Our objective is to determine the statistics of the occurrences of a set of r -letter words when the sequence is chosen as a periodic Markov chain of order ≤ r -1. We first obtain a generating function for the associated probability distribution and then display its Poisson limit. For an i.i.d. letter sequence, correction terms to the Poisson limit are given. Finally, we indicate how a hidden Markov chain fits into this scheme.

📜 SIMILAR VOLUMES

New Euler–Mahonian Statistics on Permuta

New Euler–Mahonian Statistics on Permutations and Words

✍ Robert J Clarke; Einar Steingrı́msson; Jiang Zeng 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 338 KB

We define new Mahonian statistics, called MAD, MAK, and ENV, on words. Of these, ENV is shown to equal the classical INV, that is, the number of inversions, while for permutations MAK has been already defined by Foata and Zeilberger. It Ž . Ž . is shown that the triple statistics des, MAK, MAD and e

The Garden of Words

✍ Makoto Shinkai 📂 Fiction 📅 2020 🏛 Yen On 🌐 English ⚖ 155 KB

On rainy mornings, Takao can never bring him-self to go to school-instead, he spends that time at the beautiful Shinjuku Gyoen gardens and finds a brief reprieve from everything else in his life among the trees and flowers. And on one of those mornings, he discovers a mysterious woman named Yukino i

A Generalized Mahonian Statistic on Abso

A Generalized Mahonian Statistic on Absorption Ring Mappings

✍ Don Rawlings 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 279 KB

Based on a coin-tossing scheme, a generalized Mahonian statistic is defined on absorption ring mappings and applied in obtaining combinatorial interpretations of the coefficient of q j in the expansion of > k i=1 (1+q+q 2 + } } } +q m i ). In the permutation case, the statistic coincides with one st

Statistics on the table: The history of

Statistics on the table: The history of statistical concepts and methods

✍ Andrea Rusnock 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 199 KB

The case of Francis Bacon offers rich opportunities for exploring the interface of science with politics and rhetoric, and for doing so at a critical juncture in its development. Standing at the threshold of modern science, Bacon was a preeminent spokesman for science and a polymathic writer on poli

On Statistical Limit Points and the Cons

On Statistical Limit Points and the Consistency of Statistical Convergence

✍ Jeff Connor; Jeannette Kline 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 162 KB

The Tyranny Of Words

✍ Chase, Stuart 📂 Fiction 📅 1937 🌐 English ⚖ 242 KB 👁 2 views

A popular approach to semantics in which the author discusses how to clarify the meaning of words and achieve more exact communication.