๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Theory of Quality Translations with Applications to Tilings

โœ Scribed by S.S. Ryshkov; K.A. Rybnikov Jr.

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
313 KB
Volume
18
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper , we consider a broad class of simply connected complexes that includes , for example , the face-to-face tilings of E n and S n . Along with a complex (or tiling) we consider a set แ‘ซ of qualities that individually can be assigned to the various cells or tiles of the complex , and a group แ‘ก which permutes the elements of แ‘ซ . These qualities might be colours , a set of positive real numbers or a set of af fine functions . If each ordered pair of adjacent cells is associated with a group element g แ‘ก , and a quality q แ‘ซ is assigned to any particular cell of the complex , qualities can be assigned to adjacent cells using the action of the group แ‘ก on แ‘ซ . In fact , since the complex is assumed to be simply connected , a quality can be assigned to any cell of the complex by translating qualities along paths of adjacent cells using the group action .

๐Ÿ“œ SIMILAR VOLUMES

Tiling the Integers with Translates of O
Tiling the Integers with Translates of One Finite Set
โœ Ethan M. Coven; Aaron Meyerowitz ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 115 KB

A set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a finite set to tile the integers. For sets of prime power ลฝ . size, it was solved by D. Newman 1977, J. Numbe

Translating Career Theory to Practice: T
Translating Career Theory to Practice: The Risk of Unintentional Social Injustice
โœ James P. Sampson Jr.; V. Casey Dozier; Gloria P. Colvin ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› American Counseling Association ๐ŸŒ English โš– 122 KB ๐Ÿ‘ 1 views

An important aspect of social justice involves ensuring that effective career guidance is readily accessible to all citizens. The career theory used to guide the delivery of career services can contribute to or detract from social justice. This article examines the translation of career theory to pr

Applications of Coding Theory to the Con
Applications of Coding Theory to the Construction of Modular Lattices
โœ Christine Bachoc ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 439 KB

We study self-dual codes over certain finite rings which are quotients of quadratic imaginary fields or of totally definite quaternion fields over Q. A natural weight taking two different nonzero values is defined over these rings; using invariant theory, we give a basis for the space of invariants