Babayo A.M.

Research

9A9 Composite Loube I(re) I Magic Squares Infinite Abelian Group as a Miscellany Case of the 3A3 Loube I(re) I Magic Squares Infinite Abelian Group

Article March 7, 2015

In this paper, mystic miscellaneous algebraic properties of the set of 9 × 9 Composite (Nested) Loubé ré Magic Squares are vividly visualized. And, verbatim virtuoso of algebraic properties of the 3 × 3 Loubé ré Magic Squares viz: Eigen group, Magic Sum group and Centre Pieces group viewed the algebraic properties of its 9 × 9 Composite. It is also showcased that both the 2 sets equipped with the matrix binary operation of addition form infinite additive abelian groups.

Loubere IMagic Squares Semigroups and Groups

Article February 6, 2015

This work is a pioneer investigation of semigroups and groups over the Loubéré Magic Squares. By the Loubéré Magic Squares, we understand the magic squares formed by the De La Loubéré Procedure. The set of the Loubéré Magic Squares equipped with the matrix binary operation of addition forms a semigroup if the underlining set so considered is the multi set of natural numbers; and if we consider the multi set of integer numbers as the underlined set of entries of the square, the set of the squares enclosed with the aforementioned operation forms an abelian group. The Loubéré Magic Squares are always recognized with centre piece C and magic sum M(S). We showcase that the set of the centre pieces and the set of the magic sums form respective abelian groups if both are equipped with integer numbers operation of addition. We also explicate that the set of the eigen values of the squares enclosed with the integer addition (operation) forms an abelian group. We reveal that the subelement (a terminology we introduced) Magic Squares of the Loubéré Magic Squares forms a semigroup and the Subelement Magic Squares of the Loubéré Magic Squares Group forms a group, with respect to the matrix binary operation of addition.