Exact generating function for 2-convex polygons
نویسندگان
چکیده
منابع مشابه
Exact generating function for 2-convex polygons
Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their ‘concavity index’, m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure ba...
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Department of Mathematics and Mechanics, Yerevan State University, Alex Manoogian, 1 0025 Yerevan, Armenia. [email protected]. Using the inclusion-exclusion principle and the Pleijel identity, an algorithm for calculation chord length distribution function for a bounded convex polygon is obtained. In the particular case an expression for the chord length distribution function for a rhombus is obta...
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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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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2008
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/5/055001