ENUMERATING NECKLACES WITH TRANSITIONS
Francesco Bianconi, Emanuele Brugnoli · Bulletin of the Australian Mathematical Society · 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 innbeads,kcolours andttransitions. We show that our result provides a more general solution to the problem of counting alternating (proper) colourings of the vertices of a regularn-gon.