A recursive algorithm of combinatorial difference set design for least scale number on ruler

• Published in: Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 51; no. 2; pp. 178 - 185
• Main Authors: Tang, Baoxiang, Ren, Han
• Format: Journal Article
• Language: Chinese
• Published: Hangzhou Zhejiang University 01.03.2024; Zhejiang University Press
• Subjects: Algorithms; Combinatorial analysis; combinatorial difference recursive algorithm(组合差集递推算法); Engraving; graceful labeling algorithm(优美标号算法); graceful labeling(优美标号); Graph theory; minimal graceful graph(极小优美图); ruler with least number of scales(最省刻度尺); Ticks
• ISSN: 1008-9497
• DOI: 10.3785/j.issn.1008-9497.2024.02.006

For a positive integer n≥2, what is the minimum number of ticks to be engraved on an unscaled ruler of length n to measure all lengths from 1 to n. This is an unsolved problem of ruler with least number of scales. This paper clarifies the relationship between ruler with the least number of scales and the minimal graceful graph, and a combined difference recursive algorithm for calculating all the least scale values ​​of ruler with the least number of scales is given. This algorithm calculates that the length is 3 to all the minimum scale values ​​of the most scale-saving ruler of 40, and combined with the graph theory model, the minimum scale values ​​of ruler with least number of scales with lengths from 41 to 82 are given.