Ethan P. White
Department of Mathematics
Room 121, 1984 Mathematics Road
Vancouver, BC V6T 1Z2
Richard K. Guy
Department of Mathematics and Statistics
University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4
An S-necklace of length n is a circular arrangement of the
integers 0, 1, 2, ..., n – 1 such that the absolute difference
of two neighbors always belongs to S. Focusing in particular on the
case |S| = 2, we prove that, subject to certain conditions on
the two elements in S, the number of S-necklaces obeys a
linear homogeneous recurrence relation. We give an algorithm for computing
the corresponding generating function and compute generating functions
and explicit recurrence relations for several small sets S. Our
methods extend to sets S of any size.
Full version: pdf,
(Concerned with sequences
Received February 22 2022; revised version received June 12 2022.
Published in Journal of Integer Sequences,
June 13 2022.
Journal of Integer Sequences home page