Kenichi Takemura

collaborators

3 papers

math.HO2026

A Mean Value Property in Powers of the Natural Square

Paul Jolissaint, Kenichi Takemura

Let $n \geq 1$ be an odd integer, set $m = (n - 1) /2$ and let $M$ be an $n \times n$ matrix whose coefficients are of the form $M_{i, j} = aij + bi + c j + d$ where $0 \leq i, j \leq n - 1$ . Then we pr…

math.GM2026

Algebraic Classification of All 880 Fourth-Order Magic Squares and the Discovery of Complete Alternating Magic Squares

Kenichi Takemura

In this paper, we introduce a newly defined algebraic invariant for square matrices termed the \emph{Alternating Power Difference (APD)}. The APD is defined as the signed sum of th…

math.CO2025

Alternating Power Difference and Matrix Symmetry: Closed-Form Formulas for the First Appearance Degree $m_{1}$

Kenichi Takemura

This paper focuses on an integer-valued function $f_{A} (σ) := tr (A P_{σ})$ defined uniformly from a specific square matrix $A$ of order $n$ and a permutation $σ$ on the…

A Mean Value Property in Powers of the Natural Square

Algebraic Classification of All 880 Fourth-Order Magic Squares and the Discovery of Complete Alternating Magic Squares

Alternating Power Difference and Matrix Symmetry: Closed-Form Formulas for the First Appearance Degree m1​

Alternating Power Difference and Matrix Symmetry: Closed-Form Formulas for the First Appearance Degree $m_{1}$