Shedding light on words-Reference-Cited by-同舟云学术

Shedding light on words

Published:2017 Issue:1 Volume:11 Page:216-231
ISSN:1452-8630
Container-title:Applicable Analysis and Discrete Mathematics
language:en
Short-container-title:APPL ANAL DISCRETE M

Author:

Archibald Margaret¹,Blecher Aubrey¹,Brennan Charlotte¹,Knopfmacher Arnold¹,Mansour Toufik²

Affiliation:

1. University of the Witwatersrand, School of Mathematics, The John Knopfmacher Centre for Applicable Analysis and Number Theory, Wits, Johannesburg, South Africa

2. University of Haifa, Department of Mathematics, Haifa, Israel

Abstract

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.

Publisher

National Library of Serbia

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

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2. Impulse Propagation in Compositions and Words;International Journal of Mathematics and Mathematical Sciences;2021-01-20

3. Counting water cells in bargraphs of compositions and set partitions;Applicable Analysis and Discrete Mathematics;2018