SHEDDING LIGHT ON WORDS

被引：7
|
作者：
Archibald, Margaret [1 ]
Blecher, Aubrey [1 ]
Brennan, Charlotte [1 ]
Knopfmacher, Arnold [1 ]
Mansour, Toufik [2 ]
机构：
[1] Univ Witwatersrand, Sch Math, John Knopfmacher Ctr Applicable Anal & Number The, Private Bag 3, ZA-2050 Johannesburg, South Africa
[2] Univ Haifa, Dept Math, IL-3498838 Haifa, Israel
来源：
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2017年 / 11卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Words; Generating function; Paragraphs;
D O I：
10.2298/AADM1701216A
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：216 / 231
页数：16
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