Shedding light on words

Margaret Archibald; Aubrey Blecher; Charlotte Brennan; Arnold Knopfmacher; Toufik Mansour

doi:https://doi.org/10.2298/AADM1701216A

Shedding light on words

Margaret Archibald, Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	American English
Pages (from-to)	216-231
Number of pages	86
Journal	Applicable Analysis and Discrete Mathematics
Volume	11
Issue number	1
DOIs	https://doi.org/10.2298/AADM1701216A
State	Published - 1 Apr 2017

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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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 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.",

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AU - Blecher, Aubrey

AU - Brennan, Charlotte

AU - Knopfmacher, Arnold

AU - Mansour, Toufik

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N2 - 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.

AB - 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.

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Shedding light on words

Abstract

All Science Journal Classification (ASJC) codes

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