Assignment3Questions.pdf

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9/13/2016 webhome.cs.uvic.ca/~ruskey/classes/226/Ass3_226Summer2016.html 1/3 CSC 226 Summer 2016 Assignment #3: Written part In this problem you will derive a binomial coefficient identity based on walks on a grid, starting, as usual, at the lower left corner and ending at the upper right corner, with only moves one step up and one left right allowed. Assume that the grid has rows and columns. Any path must eventually use exactly one edge in the -th column. Classify the paths according to which of the edges is used. E.g., the blue edges in the figure below; here and (counting from 0). Your identity will have the form Your job is to figure out the value of . What is the identity for the figure shown below? What number do you get if you subtract the binomial coefficients with an even from those with an odd , where

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