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Endofunctions of given cycle type |
Endofunctions of given cycle type
Jointly written with PETER SCHÖPF. The Annales des
Sciences Mathematiques du Quebec ISSN 0707-9109 23 (2),
173 - 187, 1999.
Abstract: Iteration of an endofunction f on a finite set
X defines cycles of f. To a given set L of lengths and to a given
function m: L→ ℕ0, the number of all those
functions having m(l) cycles of length l in L and possibly other
cycles of length l not in L will be computed. Furthermore by
introducing group actions the number of patterns of these functions
can be derived from the Cauchy-Frobenius Lemma. We compare these
solutions with the results derived from combinatorial species
theory.
harald.fripertinger "at" uni-graz.at, April 22,
2024
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Endofunctions of given cycle type |
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