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A123400 Infinite string related to Ehrlich's swap method for generating permutations. 3

%I #20 Jan 17 2024 04:13:52

%S 1,2,1,2,1,3,2,1,2,1,2,3,1,2,1,2,1,3,2,1,2,1,2,4,3,1,3,1,3,2,1,3,1,3,

%T 1,2,3,1,3,1,3,2,1,3,1,3,1,4,2,3,2,3,2,1,3,2,3,2,3,1,2,3,2,3,2,1,3,2,

%U 3,2,3,4,1,2,1,2,1,3,2,1,2,1,2,3,1,2,1,2,1,3,2,1,2,1,2,4,3,1,3,1,3,2,1,3,1

%N Infinite string related to Ehrlich's swap method for generating permutations.

%C In the successive permutations in star-transposition order a(n) is the position of the element swapped with the first element at step n; equivalently, the value swapped with 0 in the inverse permutation. - _Joerg Arndt_, Dec 25 2023

%C The first 24 values (plus 1, as [2, 3, 2, 3, 2, 4, 3, 2, 3, 2, 3, 4, 2, 3, 2, 3, 2, 4, 3, 2, 3, 2, 3, 5]) are given on the last page of the Kompel'makher/Liskovets reference. - _Joerg Arndt_, Jan 17 2024

%D D. E. Knuth, TAOCP, Section 7.2.1.2.

%H Joerg Arndt, <a href="/A123400/b123400.txt">Table of n, a(n) for n = 1..5039</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 10.8 "Star-transposition order", pp.257-258.

%H V. L. Kompel'makher, V. A. Liskovets, <a href="https://www.researchgate.net/profile/Timothy-Walsh-6">Sequential generation of arrangements by a basis of transpositions</a>, Cybernetics and Systems Analysis, vol. 11, no. 3, pp. 362-366, (1975).

%e permutation swap inverse permutation

%e 0: [ 0 1 2 3 ] [ 0 1 2 3 ]

%e 1: [ 1 0 2 3 ] (0, 1) [ 1 0 2 3 ]

%e 2: [ 2 0 1 3 ] (0, 2) [ 1 2 0 3 ]

%e 3: [ 0 2 1 3 ] (0, 1) [ 0 2 1 3 ]

%e 4: [ 1 2 0 3 ] (0, 2) [ 2 0 1 3 ]

%e 5: [ 2 1 0 3 ] (0, 1) [ 2 1 0 3 ]

%e 6: [ 3 1 0 2 ] (0, 3) [ 2 1 3 0 ]

%e 7: [ 0 1 3 2 ] (0, 2) [ 0 1 3 2 ]

%e 8: [ 1 0 3 2 ] (0, 1) [ 1 0 3 2 ]

%e 9: [ 3 0 1 2 ] (0, 2) [ 1 2 3 0 ]

%e 10: [ 0 3 1 2 ] (0, 1) [ 0 2 3 1 ]

%e 11: [ 1 3 0 2 ] (0, 2) [ 2 0 3 1 ]

%e 12: [ 2 3 0 1 ] (0, 3) [ 2 3 0 1 ]

%e 13: [ 3 2 0 1 ] (0, 1) [ 2 3 1 0 ]

%e 14: [ 0 2 3 1 ] (0, 2) [ 0 3 1 2 ]

%e 15: [ 2 0 3 1 ] (0, 1) [ 1 3 0 2 ]

%e 16: [ 3 0 2 1 ] (0, 2) [ 1 3 2 0 ]

%e 17: [ 0 3 2 1 ] (0, 1) [ 0 3 2 1 ]

%e 18: [ 1 3 2 0 ] (0, 3) [ 3 0 2 1 ]

%e 19: [ 2 3 1 0 ] (0, 2) [ 3 2 0 1 ]

%e 20: [ 3 2 1 0 ] (0, 1) [ 3 2 1 0 ]

%e 21: [ 1 2 3 0 ] (0, 2) [ 3 0 1 2 ]

%e 22: [ 2 1 3 0 ] (0, 1) [ 3 1 0 2 ]

%e 23: [ 3 1 2 0 ] (0, 2) [ 3 1 2 0 ]

%Y Cf. A159880 (first element in successive permutations).

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Oct 15 2006

%E More terms from _Joerg Arndt_, Apr 25 2009

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)