On the generation of necklaces and bracelets in R

Abstract

This note introduces a code snippet in R aiming to generate necklaces as well as bracelets. Among various uses, necklaces are useful tools to manage traces of products of random matrices. Functionality for necklaces and bracelets is provided with some examples of applications such as Lyndon words and de Bruijn sequences. The routines are collected in the Necklaces package available from the Comprehensive R Archive Network.

Keywords:

• Bracelet
• de Bruijn sequence
• Lyndon word
• Multi-index composition
• Necklace

Notes

1 A Maple procedure to compute these moments is available in Di Nardo and Guarino (2013).