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• W2117481519 startingPage "3213" @default.
• W2117481519 abstract "We present results for the generating functions of polygons and more general objects that can touch, constructed from two fully directed walks on the infinite triangular lattice, enumerated according to each type of step and weighted proportional to the area and the number of contacts between the directed sides of the objects. In general these directed objects are known as festoons, being constructed from the so-called friendly directed walks, while the subset constructed from vicious walks are staircase polygons, also known as parallelogram polyominoes. Additionally, we give explicit formulae for various first area-moment generating functions, that is when the area is summed over all configurations with a given perimeter. These results generalize and summarize nearly all known results on the square lattice, since such results can be obtained by setting one of the step weights to zero. All our results for the triangular lattice are new and hence provide the opportunity to study subtle changes in scaling between lattices. In most cases we give our results both in terms of ratios of infinite q-series and as continued fractions." @default.
• W2117481519 created "2016-06-24" @default.
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• W2117481519 date "2002-03-28" @default.
• W2117481519 modified "2023-10-18" @default.
• W2117481519 title "Anisotropic step, mutual contact and area weighted festoons and parallelogram polyominoes on the triangular lattice" @default.
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• W2117481519 doi "https://doi.org/10.1088/0305-4470/35/14/305" @default.
• W2117481519 hasPublicationYear "2002" @default.
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