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Abstract
A successive method of deriving the necklaces of higher lengths from the lower ones when the absolute difference of two adjacent beads (DBs) belongs to a specified set of numbers is developed. Some of them can be obtained in sequence; while others are obtained from even length to next even length, or odd length to next odd length. There are many possible necklaces for the same length. The technique is extended to DBs with different sets of numbers which include 1. Gluing method is developed which gives the higher length necklaces from lower ones by interconnecting two necklaces.
ACKNOWLEDGEMENT
The author wishes to thank the reviewers for their constructive suggestions which helped improving the presentation of the paper.
DISCLOSURE STATEMENT
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Tejmal Rathore
T S Rathore served SGSITS Indore (1965–1978), IIT Bombay, (1978–2006), SFIT, Mumbai (2006–2014), and IIT Goa (2017–2019). He was a PDF at Concordia University (1983–1985) and a researcher at University of South Australia (1993). He was an ISTE visiting professor for two years. He is the author of Digital Measurement Techniques; the book has been translated in Russian and Hindi. He is the co-author of Network Analysis by Van Valkenburg. He was the Guest Editor of the Journal of Inst of Engineers on Instrumentation Electronics (1991) and Editor for IETE Journal of Education for one term of five years. Prof. Rathore is an LSM of IEEE, Fellow of IETE and IE, Member of ISTE, Instrument and Computer Societies of India. He has received IEEE Silver Jubilee Medal, and several awards from IETE and ISTE.