SHIFT TRANSFORM APPROACH TO THE TWO-SIDED BALLOT THEOREM

Authors : Kubilay DAGTOROS

Pages : 1-7

Doi:10.54559/jauist.1070936

View : 10 | Download : 6

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :We present a recursive formula for the two-sided ballot theorem using left and right shift transforms. In particular, we showed that the xth entry of the image of the d + 1 dimensional unit vector under the sum of the left and right shift operators is the number of walks in the lattice interval [0,d] that start at the origin and stop at the location x. This approach enables us to write a recursive formula for the number of possible n−walks between two obstacles that stop at a predetermined location.
Keywords : ballot theorem, random walk, self avoiding walk, reflection method