#####
Séminaire Lotharingien de Combinatoire, B21b (1989), 11
pp.

[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 413/S-21, p.
19-31.]

# Andreas Dress and Christian Siebeneicher

# Zur Abzählung periodischer Worte

**Abstract.**
We show that the basic bijection *\Psi*
of a diagram which has been introduced in
[DS3] (see also [DS2]) to unify the known combinatorial
proofs of the so called *cyclotomic identity*
(cf. [DS1,MR1,MR2,VW]) and which provides
moreover a setting for bijections concerning primitive
necklaces, defined and studied by
Viennot [V],
de Bruijn and Klarner [dBK], and Gessel [DW],
may be viewed as a special instance of a
more general bijection defined for arbitrary
*cyclic sets*. Indeed, if this more general bijection is applied
to the cyclic set *P*(*A*) of
periodic functions on the integers with values in the set
*A*, one gets the bijection discussed in [DS2,DS3].

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