- Journal of Amasya University the Institute Sciences and Technology
- Vol: 3 Issue: 1
- SHIFT TRANSFORM APPROACH TO THE TWO-SIDED BALLOT THEOREM
SHIFT TRANSFORM APPROACH TO THE TWO-SIDED BALLOT THEOREM
Authors : Kubilay Dagtoros
Pages : 1-7
Doi:10.54559/jauist.1070936
View : 13 | Download : 4
Publication Date : 2022-06-30
Article Type : Research
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.