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

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 an...

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Vydané v:	Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Ročník 51; číslo 2; s. 178 - 185
Hlavní autori:	Tang, Baoxiang, Ren, Han
Médium:	Journal Article
Jazyk:	Chinese
Vydavateľské údaje:	Hangzhou Zhejiang University 01.03.2024 Zhejiang University Press
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1008-9497
DOI:	10.3785/j.issn.1008-9497.2024.02.006