What question did this study set out to answer?

The aim is to establish the growth class for singly-even magic-square orders, particularly at n=6.

July 10, 20260 citationsOpen Access

The growth class of the magic-square count, reached in the hardest singly-even regime

LMLohans de Oliveira Miranda LMLossian Barbosa Bacelar MirandaInstituto Federal do Piauí

Key Points

The aim is to establish the growth class for singly-even magic-square orders, particularly at n=6.
Developed closed-form lower bounds for growth class in singly-even magic-square orders.
Analyzed the previously unexplored singly-even orders in this context.
First established growth order for singly-even magic squares such as Euler's 36-ocers at order n=6.
Brought singly-even orders into a comparable analytical framework as doubly-even orders.

Abstract

For the doubly-even orders a program of closed-form lower bounds of the correct growth order is by now established (ChenGrigorescu; Oboudi; TiamkaewSaethaoSingha); for the singly-even orders classically the hardest, home of Euler's 36-ocers order n= 6 none was known. We supply, to our knowledge, the 1rst, bringing the hard class into the same attackable territory.

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