A $$d$$ d -dimensional Extension of Christoffel Words
نویسندگان
چکیده
منابع مشابه
A d-dimensional extension of Christoffel words
In this article, we extend the definition of Christoffel words to directed subgraphs of the hypercubic lattice in arbitrary dimension that we call Christoffel graphs. Christoffel graphs when d = 2 correspond to well-known Christoffel words. Due to periodicity, the d-dimensional Christoffel graph can be embedded in a (d−1)-torus (a parallelogram when d = 3). We show that Christoffel graphs have ...
متن کاملOn a generalization of Christoffel words: epichristoffel words
Sturmian sequences are well-known as the ones having minimal complexity over a 2-letter alphabet. They are also the balanced sequences over a 2-letter alphabet and the sequences describing discrete lines. They are famous and have been extensively studied since the 18th century. One of the generalization of these sequences are the episturmian sequences, introduced by A. de Luca [dL97a] and studi...
متن کاملA non trivial extension of the two - dimensional Ising model : the d - dimensional “ molecular ” model . Fabio
A recently proposed molecular model is discussed as a non-trivial extension of the Ising model. For d = 2 the two models are shown to be equivalent, while for d > 2 the molecular model describes a peculiar second order transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. The general mean field analysis is compared with the results achieved ...
متن کاملChristoffel Words and the Calkin-Wilf Tree
In this note we present some results on the Calkin-Wilf tree of irreducible fractions, giving an insight on the duality relating it to the Stern-Brocot tree, and proving noncommutative versions of known results relating labels of the CalkinWilf trees to hyperbinary expansions of positive integers. The main tool is the Christoffel tree introduced in a paper by Berstel and de Luca.
متن کاملFrom d-dimensional Quantum to d+ 1-dimensional Classical Systems
I review the mapping from the partition function of a d-dimensional quantum system to that of a d+ 1-dimensional classical system and I apply it to several models, in particular the classical 1d Ising, 2d XY, and 3d Ising models. These examples respectively illustrate the general features of the classical/quantum correspondence, a Berry phase term, and the role of gauge constraints. The limitat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2015
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-015-9681-2