An algorithm for counting domino tilings of a rectangular chessboard
Magomedov A.M. Lawrence S.A.
22 December 2025Jacodesmath Institute
Journal of Algebra Combinatorics Discrete Structures and Applications
2025#13Issue 115 - 27 pp.
A recursive method is developed for counting domino tilings of a rectangular chessboard (the dimer problem). Based on this method, a new and enhanced recursive algorithm is proposed for solving this problem. Close connections with Fibonacci numbers are traced out.
05B45 , 11B39 , 52C20 , Algorithm , Dimer problem , Domino tiling , Fibonacci numbers , Recurrence relation , Tiling counting
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Department of Discrete Mathematics and Informatics, Dagestan State University, Department of Mathematics and Informatics, Dagestan Federal Research Center of the Russian Academy of Sciences, 45 M. Gadzhiev, Dagestan, Makhachkala, 367032, Russian Federation
Department of Cryptology, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satbaev, Astana, 10000, Kazakhstan
Institute of Service Technologies, Russian State University of Tourism and Service, Podolsk, Russian Federation
Department of Discrete Mathematics and Informatics
Department of Cryptology
Institute of Service Technologies
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