TITLE:
Algebra and Geometry of Sets in Boolean Space
AUTHORS:
Vladimir Leontiev, Garib Movsisyan, Zhirayr Margaryan
KEYWORDS:
Equations on Sets, Hausdorff Distance, Hamming Distance, Generating Function, Minkowski Sum, Sum of Sets
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.6 No.2,
March
31,
2016
ABSTRACT: In the
present paper, geometry of the Boolean space Bn in terms of Hausdorff distances between subsets and
subset sums is investigated. The main results are the algebraic and analytical
expressions for representing of classical figures in Bn and the functions of distances between them. In
particular, equations in sets are considered and their interpretations in
combinatory terms are given.