On Self-Descriptive Squares

TL;DR

This paper introduces a new class of self-referential square matrices where some entries record the frequency of numbers within the matrix, revealing intriguing cases like algebraic and magic squares with self-descriptive properties.

Contribution

It defines and explores a novel type of self-descriptive squares, including their algebraic and magic variants, expanding the understanding of self-referential matrix structures.

Findings

Identification of self-descriptive squares that are also magic squares

Existence of algebraic variable-inclusive self-descriptive squares

Characterization of elusive properties of these matrices

Abstract

A novel kind of self-referential square matrix is introduced. A certain subset of the matrix entries record the frequencies of occurrence of each distinct number appearing within the entire matrix. Such squares are necessarily elusive. Our investigation brings to light interesting cases, such as 'generic' squares that include algebraic variables and self-descriptive squares that are also magic squares.