부산대학교 도서관

Summary: ``We study the area distribution of closed walks of length$n$, starting and ending at the origin. The concept of algebraic areaof a walk in the square lattice is slightly modified and the usefulnessof this concept is demonstrated through a simple argument. The idea ofusing a generating function of the form $(x+x^{-1}+y+y^{-1})^n$ tostudy these walks is then discussed from a special viewpoint. Based onthis, a polynomial time algorithm for calculating the exactdistribution of such walks for a given length, is concluded. Thepresented algorithm takes advantage of the Chinese remainder theorem toovercome the problem of arithmetic with large integers. Finally, theresults of the implementation are given for $n=32, 64, 128$.''