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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