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Explore recent theoretical developments in quasi-crystals and their applications in combinatorics through this 47-minute conference talk delivered at ICBS2025 by BIMSA. Delve into the mathematical foundations of quasi-crystalline structures, examining their unique properties that distinguish them from traditional periodic crystals. Learn about cutting-edge advances in quasi-crystal theory and discover how these mathematical concepts translate into practical combinatorial applications. Gain insights into the intersection of crystallography, mathematics, and combinatorial analysis as the speaker presents current research findings and theoretical breakthroughs in this specialized field of study.