Part III: Contributed Papers New Results On Graphs And Combinatorics

Graphs and Combinatorics

Volume 406 of the series Lecture Notes in Mathematics pp 339-349


The charm bracelet problem and its applications

  • Paul K. StockmeyerAffiliated withCollege of William and Mary

* Final gross prices may vary according to local VAT.

Get Access


The necklace problem has proved to be both a sound pedagogical device in teaching enumeration theory and a valuable counting tool with several graphical applications. In this paper we solve the more general charm bracelet problem and provide two applications for which the necklace problem in not sufficient.

We set the stage in Section 1 by providing a brief review of the necklace problem. This serves as a basis for comparison in Section 2, where we discuss the charm bracelet problem and derive its solution. Sections 3 and 4 contain nontrivial graphical applications of the results of Section 2.

Definitions for all graphical terms and concepts can be found in [3]. For further background and broader treatment of topics of an enumerative nature, [5] should be consulted.