The perimeter generating function of punctured staircase polygons
نویسندگان
چکیده
منابع مشابه
The perimeter generating function of punctured staircase polygons
Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of punctured staircase polygons (staircase polygons with a single internal staircase hole). We find that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We perform an analysis of the properties of the differ...
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We have derived the perimeter generating function of a model of punctured staircase polygons in which the internal staircase polygon is rotated by a 90◦ angle with respect to the outer staircase polygon. In one approach we calculated a long series expansion for the problem and found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of o...
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We have derived the perimeter generating function of a model of punctured staircase polygons in which the internal staircase polygon is rotated by a 90° angle with respect to the outer staircase polygon. In one approach we calculated a long series expansion for the problem and found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of o...
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An explicit expression is obtained for the perimeter and area generating function G(y, z) = ∑ n>=2 ∑ m>=1 cn,my z, where cn,m is the number of row-convex polygons with area m and perimeter n. A similar expression is obtained for the area-perimeter generating function for staircase polygons. Both expressions contain q-series.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2006
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/39/15/002