每一個凸n星形皆可決定唯一的一個排列sigma，
其內角和由此排列sigma來決定。
在此論文中，我們給出了一個公式去計算凸
n星形之內角和；並且利用此公式去推導出一個
遞迴關係式，此關係式可用來計算具有某特定值的內角和之凸n星形的個數。

Every (convex) star polygon with n vertices can be associated with a permutation on {1,2, . . . , n } . It is known that the sum of interior angles of the polygon is solely
determined by ˙. In this thesis, we give an exact formula to calculate the sum of
interior angles in term of ˙. We make use of this formula to derive a recurrence
relation concerning the number of star polygons having a particular value of sums
of interior angles.

1. Introduction 3
2. Notations and preliminary results 4
3. Main results 9
References 16

[1]A. Bezdek and F. Fodor, "On convex polygons of maximal width", Arch.Math. 74 (2000).
[2]J.W. Archbold, "Algebra", 4th edition, Pitman, London, (1970)