Abstract

MORALES, César Andrés; MUNOZ, José Herman  and  RODRIGUEZ, Miguel Armando. Recurrence patterns in the k-mino game. Rev. Mat [online]. 2019, vol.26, n.1, pp.115-138. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v26i1.35526.

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In this work we study two generalizations to the double-6 domino tiles. In a general way, it is considered the k-mino, (k, n), which consists in combining the numbers from 0 to n in groups of k. With this approach and using a new procedure it is found interesting recurrence patterns in function of the k and n parameters in order to obtain the number of pieces and the sum of the score of all pieces of the mentioned game. In a sequen- tial way it is studied the domino (2, n) and the trimino P (3, n) in order to generalize to (k, n). The obtained results are related with the Pas- cal’s triangle and another mathematical topics as combinatorial, numerical sequences and series of higher-order, symmetric matrices, symmetric ten- sors, and complete graphs.

Keywords : domino; Pascal’s triangle; sequences; series.

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