Sums of Angles of Star Polygons and the Eulerian Num- bers
نویسندگان
چکیده
Every (convex) star polygon with n vertices can be associated with a permutation σ on {1, 2, . . . , n}. We give an exact formula to compute the sum of (interior) angles in term of σ. In particular, the sum of angles of the polygon is solely determined by σ. We make use of this formula to derive a recurrence relation concerning the number of star polygons having a particular value of sums of angles. The results are summarized in a Pascal type triangle. By observing the relation of such numbers and the Eulerian numbers, we obtain a closed formula. A possible application to quantum physics is presented.
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تاریخ انتشار 2004