3,392 research outputs found
On Generating Binary Words Palindromically
We regard a finite word up to word isomorphism as an
equivalence relation on where is equivalent to if
and only if Some finite words (in particular all binary words) are
generated by "{\it palindromic}" relations of the form for some
choice of and That is to say,
some finite words are uniquely determined up to word isomorphism by the
position and length of some of its palindromic factors. In this paper we study
the function defined as the least number of palindromic relations
required to generate We show that every aperiodic infinite word must
contain a factor with and that some infinite words have
the property that for each factor of We obtain a
complete classification of such words on a binary alphabet (which includes the
well known class of Sturmian words). In contrast for the Thue-Morse word, we
show that the function is unbounded
Transition Property For Cube-Free Words
We study cube-free words over arbitrary non-unary finite alphabets and prove
the following structural property: for every pair of -ary cube-free
words, if can be infinitely extended to the right and can be infinitely
extended to the left respecting the cube-freeness property, then there exists a
"transition" word over the same alphabet such that is cube free. The
crucial case is the case of the binary alphabet, analyzed in the central part
of the paper.
The obtained "transition property", together with the developed technique,
allowed us to solve cube-free versions of three old open problems by Restivo
and Salemi. Besides, it has some further implications for combinatorics on
words; e.g., it implies the existence of infinite cube-free words of very big
subword (factor) complexity.Comment: 14 pages, 5 figure
Periods and Borders of Random Words
We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length k is a constant, depending only on k and the alphabet size l. We give a recurrence that allows us to determine these constants with any required precision. This also allows us to evaluate the expected period of a random word. For the binary case, the expected period is asymptotically about n-1.641. We also give explicit formulas for the probability that a random word is unbordered or has maximum border length one
Understanding maximal repetitions in strings
The cornerstone of any algorithm computing all repetitions in a string of
length n in O(n) time is the fact that the number of runs (or maximal
repetitions) is O(n). We give a simple proof of this result. As a consequence
of our approach, the stronger result concerning the linearity of the sum of
exponents of all runs follows easily
From the mountains to the prairies and beyond the pale : American yodeling on early recordings
This sound review surveys yodeling in North American popular music, beginning with some of the earliest recordings on which it is featured. In order to better contextualize the recordings, I will also mention a few examples of sheet music with yodelingâitems which are generally overlooked. My intention is to question why yodeling became attached to particular genres and how it functions in the construction of those genres. Indeed, two popular music genresâso-called hillbilly music and cowboy or Western musicâmade yodeling an important, if not identifying, component. The focus here is on yodelingâs connotations and associations and how these established expressive relationships between the moods, personae, and images of the songs
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