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Restricted growth functions for set partitions.
7

%I #28 Dec 14 2022 09:50:07

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

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

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

%N Restricted growth functions for set partitions.

%C There are restricted growth functions (RGF, sometime called restricted growth strings, RGS) for various kinds of combinatorial objects. For the RGF used here see figure 17.1-D on p.358 of the Fxtbook, see links.

%H Alois P. Heinz, <a href="/A120698/b120698.txt">Rows n = 1..5295, flattened</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>

%e Table starts:

%e 1

%e 1,1

%e 1,2

%e 1,1,1

%e 1,1,2

%e 1,2,1

%e 1,2,2

%e 1,2,3

%t Flatten[Table[RGFs[n],{n,1,5}]](* _Geoffrey Critzer_, Dec 08 2010 *)

%Y Cf. A000110, A085693 (row maxima), A120699 (row lengths), A193023.

%K nonn,tabf

%O 1,5

%A _Franklin T. Adams-Watters_, Jun 28 2006