On Operations Preserving Primitivity of Partial Words with One Hole

نویسندگان

  • Francine Blanchet-Sadri
  • Sarah Nelson
  • Amelia Tebbe
چکیده

The notion of a primitive word, one that is not a power of another word, is useful in many areas including coding theory, combinatorics on words, formal language theory, and text algorithms. The proportion of such words turns out to be very high. We investigate operations that preserve the primitivity of partial words with one hole, or words that have an undefined position. As a result, all primitive binary partial words with one hole of length up to 11 can be generated.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Exchange-Robust and Subst-Robust Primitive Partial Words

A partial word is a word that may have some unknown places known as “holes” and can be replaced by the symbols from the underlying alphabet. A partial word u is said to be primitive if there does not exist a word v such that u is contained in a nontrivial integer power of v. We study the preservation of primitivity in partial words by the effect of some point mutation operations. In this paper,...

متن کامل

Some operations preserving primitivity of words

We investigate some operations where essentially, from a given word w, the word ww′ is constructed where w′ is a modified copy of w or a modified mirror image of w. We study whether ww′ is a primitive word provided that w is primitive. For instance, we determine all cases with an edit distance of w and w′ at most 2 such that the primitivity of w implies the primitivity of ww′. The operations ar...

متن کامل

Testing primitivity on partial words

Primitive words, or strings over a finite alphabet that cannot be written as a power of another string, play an important role in numerous research areas including formal language theory, coding theory, and combinatorics on words. Testing whether or not a word is primitive can be done in linear time in the length of the word. Indeed, a word is primitive if and only if it is not an inside factor...

متن کامل

Primitivity Preserving Endomorphisms of Free Groups

An endomorphism φ of a free group is called primitivity preserving if φ takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank n ≥ 3 is an automorphism.

متن کامل

Finite Plate with Circular and Square Hole under Partial Loading

In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the parti...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011