منابع مشابه
Linear Magic Rectangles
Our purpose is to introduce a linear-algebraic construction for magic rectangles of size pr × ps, where p is prime and 1 ≤ r ≤ s. For fixed p, r, and s, this method allows for the production of many different magic rectangles. It follows that, for many non-coprime dimensions, this construction will significantly augment the sparse collection of “known” magic rectangles. A magic rectangle of siz...
متن کاملConstruction of magic rectangles of odd order
Magic rectangles are well-known for their very interesting and entertaining combinatorics. Such magic rectangles have also been used in designing experiments. In a magic rectangle, the integers 1 to pq are arranged in an array of p rows and q columns so that each row adds to the same total P and each column to the same total Q. In the present paper we provide a systematic method for constructin...
متن کاملA matrix approach to construct magic rectangles of even order
Magic rectangles are well-known for its very interesting and entertaining combinatorics. In a magic rectangle, the numbers 1 to mn are arranged in an array of m rows and n columns so that each row adds to the same total M and each column to the same total N . In the present paper we provide a new systematic method for constructing any even by even magic rectangle. The method proposed is extreme...
متن کاملDual Rectangles
This article concerns a notion of duality between rectangles. A proof is given that only finitely many integral sided pairs of dual rectangles exist. Then a geometrical group law is shown to hold on the set of all rational self-dual rectangles. Finally, the arithmetic of a cubic surface is used to construct new pairs of rational dual rectangles from old, a technique inspired by the theory of el...
متن کاملMeasurable Rectangles
We give an example of a measurable set E ⊆ R such that the set E ′ = {(x, y) : x + y ∈ E} is not in the σ-algebra generated by the rectangles with measurable sides. We also prove a stronger result that there exists an analytic (Σ11) set E such that E ′ is not in the σ-algebra generated by rectangles whose horizontal side is measurable and vertical side is arbitrary. The same results are true wh...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2019
ISSN: 1063-8539,1520-6610
DOI: 10.1002/jcd.21667