SHIFT TRANSFORM APPROACH TO THE TWO-SIDED BALLOT THEOREM

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Journal of Amasya University the Institute Sciences and Technology
Volume:3 Issue:1
SHIFT TRANSFORM APPROACH TO THE TWO-SIDED BALLOT THEOREM

SHIFT TRANSFORM APPROACH TO THE TWO-SIDED BALLOT THEOREM

Pages : 1-7

View : 50 | Download : 11

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

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