A word over an alphabet [k] can be represented by a bargraph, where the height of the i-th column is the size of the i-th part. If North is in the direction of the positive y-axis and East is in the direction of the positive x-axis, a light source projects parallel rays from the North-West direction, at an angle of 45 degrees to the y-axis. These rays strike the cells of the bargraph. We say a cell is lit if the rays strike its West facing edge or North facing edge or both. With the use of matrix algebra we fund the generating function that counts the number of lit cells. From this we nd the average number of lit cells in a word of length n.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics