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ENUMERATING NECKLACES WITH TRANSITIONS
Published online by Cambridge University Press: 11 May 2021
Abstract
Necklaces are the equivalence classes of words under the action of the cyclic group. Let a transition in a word be any change between two adjacent letters modulo the word’s length. We present a closed-form solution for the enumeration of necklaces in n beads, k colours and t transitions. We show that our result provides a more general solution to the problem of counting alternating (proper) colourings of the vertices of a regular n-gon.
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- Research Article
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- © 2021 Australian Mathematical Publishing Association Inc.
Footnotes
Partially supported by the Department of Engineering, Università degli Studi di Perugia, Italy, within the project Artificial Intelligence for Earth Observation (Fundamental Research Grant Scheme 2020).