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In this paper we present a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted au-tomata, equations of ordinary generating functions and continued fractions. It is a variation of the(More)
In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. We associate with this family of words a family of curves that are like the Fibonacci word fractal and reveal some fractal features. Finally, we describe an infinite family of polyominoes stems from the generalized Fibonacci(More)
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