843 research outputs found
A lower bound for Garsia's entropy for certain Bernoulli convolutions
Let be a Pisot number and let denote Garsia's
entropy for the Bernoulli convolution associated with . Garsia, in 1963
showed that for any Pisot . For the Pisot numbers which
satisfy (with ) Garsia's entropy has been
evaluated with high precision by Alexander and Zagier and later improved by
Grabner, Kirschenhofer and Tichy, and it proves to be close to 1. No other
numerical values for are known.
In the present paper we show that for all Pisot , and
improve this lower bound for certain ranges of . Our method is
computational in nature.Comment: 16 pages, 4 figure
A Characterization of Infinite LSP Words
G. Fici proved that a finite word has a minimal suffix automaton if and only
if all its left special factors occur as prefixes. He called LSP all finite and
infinite words having this latter property. We characterize here infinite LSP
words in terms of -adicity. More precisely we provide a finite set of
morphisms and an automaton such that an infinite word is LSP if
and only if it is -adic and all its directive words are recognizable by
A context-free and a 1-counter geodesic language for a Baumslag-Solitar group
We give a language of unique geodesic normal forms for the Baumslag-Solitar
group BS(1,2) that is context-free and 1-counter. We discuss the classes of
context-free, 1-counter and counter languages, and explain how they are
inter-related
A Coloring Problem for Sturmian and Episturmian Words
We consider the following open question in the spirit of Ramsey theory: Given
an aperiodic infinite word , does there exist a finite coloring of its
factors such that no factorization of is monochromatic? We show that such a
coloring always exists whenever is a Sturmian word or a standard
episturmian word
Finite automata for testing uniqueness of Eulerian trails
We investigate the condition under which the Eulerian trail of a digraph is
unique, and design a finite automaton to examine it. The algorithm is
effective, for if the condition is violated, it will be noticed immediately
without the need to trace through the whole trail
k-Spectra of weakly-c-Balanced Words
A word is a scattered factor of if can be obtained from by
deleting some of its letters. That is, there exist the (potentially empty)
words , and such that and
. We consider the set of length- scattered
factors of a given word w, called here -spectrum and denoted
\ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w)
for binary strictly balanced and, respectively, -balanced words , i.e.,
words over a two-letter alphabet where the number of occurrences of each letter
is the same, or, respectively, one letter has -more occurrences than the
other. In particular, we consider the question which cardinalities n=
|\ScatFact_k(w)| are obtainable, for a positive integer , when is
either a strictly balanced binary word of length , or a -balanced binary
word of length . We also consider the problem of reconstructing words
from their -spectra
Avoidability of formulas with two variables
In combinatorics on words, a word over an alphabet is said to
avoid a pattern over an alphabet of variables if there is no
factor of such that where is a
non-erasing morphism. A pattern is said to be -avoidable if there exists
an infinite word over a -letter alphabet that avoids . We consider the
patterns such that at most two variables appear at least twice, or
equivalently, the formulas with at most two variables. For each such formula,
we determine whether it is -avoidable, and if it is -avoidable, we
determine whether it is avoided by exponentially many binary words
Pairwise Well-Formed Modes and Transformations
One of the most significant attitudinal shifts in the history of music
occurred in the Renaissance, when an emerging triadic consciousness moved
musicians towards a new scalar formation that placed major thirds on a par with
perfect fifths. In this paper we revisit the confrontation between the two
idealized scalar and modal conceptions, that of the ancient and medieval world
and that of the early modern world, associated especially with Zarlino. We do
this at an abstract level, in the language of algebraic combinatorics on words.
In scale theory the juxtaposition is between well-formed and pairwise
well-formed scales and modes, expressed in terms of Christoffel words or
standard words and their conjugates, and the special Sturmian morphisms that
generate them. Pairwise well-formed scales are encoded by words over a
three-letter alphabet, and in our generalization we introduce special positive
automorphisms of , the free group over three letters.Comment: 12 pages, 3 figures, paper presented at the MCM2017 at UNAM in Mexico
City on June 27, 2017, keywords: pairwise well-formed scales and modes,
well-formed scales and modes, well-formed words, Christoffel words, standard
words, central words, algebraic combinatorics on words, special Sturmian
morphism
Schweizer Volksmusik Sammlung. Die Tanzmusik der Schweiz des 19. und der ersten Hälfte des 20. Jahrhunderts, gesammelt von Hanny Christen
Voilà le fruit d’une vaste entreprise menée conjointement et courageusement par la Société pour la musique populaire en Suisse et les éditions Mülirad de Zürich. Il fallait en effet une bonne dose d’audace pour publier les travaux de collecte de la folkloriste Hanny Christen (1899-1976), puisque le corpus comprend plus de 10000 pièces musicales, ce qui donne un ensemble de 11 volumes de format 30x22 cm, chacun dans une belle reliure rigide. Ce travail éditorial, dont la direction a été confié..
Les Musiques Traditionnelles en Suisse Romande, tout au long du XXe siècle… et au tout début du XXIe !
Ce double CD constitue la première publication de la « Fondation pour les Musiques Traditionnelles Romandes» récemment créée. En quarante-deux plages, il offre un véritable et bien complet panorama des musiques traditionnelles en Suisse romande. Le pluriel s’impose ici, comme le fait remarquer Nikita Pfister dans sa notice, car il s’agit pour les membres de la Fondation de ne pas se laisser enfermer dans une quelconque définition restrictive de la notion de musique traditionnelle, mais de don..
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