Open AccessShedding light on words
Author(s) -
Margaret Archibald,
Aubrey Blecher,
Charlotte Brennan,
Arnold Knopfmacher,
Toufik Mansour
Publication year - 2017
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm1701216a
Subject(s) - alphabet , mathematics , matrix (chemical analysis) , enhanced data rates for gsm evolution , word (group theory) , column (typography) , function (biology) , combinatorics , geometry , linguistics , computer science , artificial intelligence , connection (principal bundle) , chemistry , philosophy , evolutionary biology , biology , chromatography
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 find the generating function that counts the number of lit cells. From this we find the average number of lit cells in a word of length n.