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Counting Bordered and Primitive Words with a Fixed Weight

Tero Harju, Dirk Nowotka, Counting Bordered and Primitive Words with a Fixed Weight. TUCS Technical Reports 630, Turku Centre for Computer Science, 2004.

Abstract:

A word <i>w</i> is primitive if it is not a proper power of another word,
and <i>w</i> is unbordered if it has no prefix that is also a suffix
of <i>w</i>.
We study the number of primitive and unbordered words <i>w</i>
with a fixed weight, that is, words for which the Parikh vector
of <i>w</i> is a fixed vector.
Moreover, we estimate the number of words that have a~unique border.

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BibTeX entry:

@TECHREPORT{tHaNo04b,
  title = {Counting Bordered and Primitive Words with a Fixed Weight},
  author = {Harju, Tero and Nowotka, Dirk},
  number = {630},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2004},
  keywords = {combinatorics on words, borders, primitive words},
  ISBN = {952-12-1444-9},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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