Counting Colorful Necklaces and Bracelets in Three Colors
Combinatorics
2019-03-06 v2
Abstract
A necklace or bracelet is \textit{colorful} if no pair of adjacent beads are the same color. In addition, two necklaces are \textit{equivalent} if one results from the other by permuting its colors, and two bracelets are \textit{equivalent} if one results from the other by either permuting its colors or reversing the order of the beads; a bracelet is thus a necklace that can be turned over. This note counts the number of non-equivalent colorful necklaces and the number of colorful bracelets formed with -beads in at most three colors. Expressions obtained for simplify expressions given by OEIS sequence A114438, while the expressions given for appear to be new and are not included in OEIS.
Keywords
Cite
@article{arxiv.1901.10703,
title = {Counting Colorful Necklaces and Bracelets in Three Colors},
author = {Dennis S. Bernstein and Omran Kouba},
journal= {arXiv preprint arXiv:1901.10703},
year = {2019}
}
Comments
19 pages, 2 figures