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Hyper‐rook Domain Inequalities
Author(s) -
Carnielli Walter A.
Publication year - 1990
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm199082159
Subject(s) - mathematics , domain (mathematical analysis) , dimension (graph theory) , combinatorics , hamming distance , radius , upper and lower bounds , space (punctuation) , spheres , hamming code , element (criminal law) , center (category theory) , mathematical analysis , algorithm , physics , computer science , block code , computer security , astronomy , political science , law , decoding methods , chemistry , crystallography , operating system
A hyper‐rook domain of an element x in the space (words of length n over alphabets with k elements) is a sphere with center x and fixed radius j in Hamming distance. The number j determines the dimension of the hyper‐rook domain. The classical (and far from solved) problem of covering by rook domains (here considered as the 1‐dimensional case) is the problem of finding minimal coverings of by such spheres. Very few results are known in the literature for dimensions ≥ 2. We prove in this paper certain classes of inequalities based on coverings using matrices, which give upper and lower bounds for several cases of the problem for higher dimensions.