As you know in phlethystic composition we need to "stretch" a given series.
Let T=N^(N) denote the set of finite sequences of natural numbers. A
cycle index series is a formal power series in infinitely many
variables, or in other words it is a function from N^(N) to Q (where Q
are the rationals).
Let us define an action of (N, T) -> T by (k, t) +-> kt where (kt)(n) :=
t(k*n).
Now let s: N^(N) -> Q be such a series. Then the *k-th stretch* kf of f
is defined by (ks)(t) = s(kt).
To say things in a more intuitive language: if f(x_1, x_2, x_3, ...) is
a formal power series in infinitely many variables, the k-th stretch is
f(x_{k}, x_{2k}, x_{3k}, ...).
Of course, I have "invented" the term "stretch". Does somebody know a
better name for that operation or is there even a common name that is
already used in the context of cycle index series?
Suggestions are welcome.
Thanks
Ralf
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