[math-fun] permuting via rational functions
It seems this question by D.Asimov was studied already by L.Redei: Acta Sci Math Szeged 11 (1946) 85-92 R.Nobauer: Acta Sci Math Szeged 50 (1986) 287-298 W. Nobauer: Period. Math. Hungar. 17 (1986) 37-44. (all in German) perhaps DA will be so kind as to report what they did? This one in English apparently has something to do with it too: Leonard Carlitz: A note on permutation functions over a finite field, Duke Math. J. 29 (1962) 325-332.
This one in English apparently has something to do with it too:
Leonard Carlitz: A note on permutation functions over a finite field, Duke Math. J. 29 (1962) 325-332.
--It seems Carlitz invented pretty much the same idea RC Schroeppel had posted earlier about generating permutations via polynomials, as is revealed by reading this nice paper: Michael E. Zieve: On a theorem of Carlitz, J. Group Theory 17 (2014) 667-669 http://arxiv.org/abs/0810.2834 -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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Warren D Smith