Search results for "Generating functions"

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General Solution of a Second-Order Nonhomogenous Linear Difference Equation with Noncommutative Coefficients

2010

The detailed construction of the general solution of a second-order nonhomogenous linear operator-difference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by studying some applications belonging to different mathematical contexts.

Difference equation noncommutativity companion matrix generating functions
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Enumeration of L-convex polyominoes by rows and columns

2005

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.

Discrete mathematicsRecurrence relationECO methodGeneral Computer SciencePolyominoGenerating functionRegular polygonRow and column spacesTheoretical Computer ScienceInterpretation (model theory)Generating functionsCombinatoricsSection (fiber bundle)Path (graph theory)Convex polyominoesComputer Science(all)MathematicsTheoretical Computer Science
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