Block-Wise Construction of Trimagic Squares with Trimagic Blocks of Orders 12 and 24 (20736)
Year: 2026
Type: preprint
Abstract: Ordinary compounds of retained normal trimagic seeds produce large normal trimagic squares with translated trimagic blocks and distinct block constants. We give a complete moment proof, establish associativity in the explicit coordinate convention, and specialize the block constants to orders twelve and twenty-four. The recorded inventory comprises fourteen construction records, including seeds, auxiliary complementary products and final compounds through complete order 20736. The principal order-twelve block family is separated from order-twenty-four branches whose aligned order-twelve pieces fail magicity. Two auxiliary trimagic arrays explain the complete orders 10368 and 17280. A newly reconstructed order-144 example verifies the displayed order-twelve seed and compound rule, while the larger computational results are attributed to their retained records. Text and Excel files of complete work are attahced.
Author: Inder J. Taneja
Institution: Universidade Federal de Santa Catarina
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225330014