Cheers Neil,

Here comes 12 new PRE_NUMBERED sequences:
A072088-A072095 & A072619-A072622,
minor COMMENTS to two sequences: A057117 & A057118,
and ADDITIONS to the INDEX-ENTRY.


---------------------------------------------------------------

Additions to the index-entry
http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation
subsection "Catalan automorphisms":

(I have continued to fill it from the fourth such line,
after the lonely A071659-A071660 pair):

permutations, of the integers, induced by Catalan automorphisms, each paired with its inverse: (4) A071659-A071660, A072090-A072091, A072092-A072093, A072094-A072095, A072619-A072620, A072621-A072622
permutations, of the integers, induced by Catalan automorphisms, each paired with its inverse: (5) A072088-A072089


-------------------------------------------------------------------------

Just ADD the next %H and %Y-lines to A057117 and A057118, and CHANGE the
name of A057118:


%I A057117
%S A057117 0,1,2,3,4,5,7,8,6,9,10,12,13,11,17,18,21,22,20,14,15,16,19,23,24,26,
%H A057117 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%Y A057117 Restriction of the automorphism A072088 to the plane binary trees.


%I A057118 
%S A057118 0,1,2,3,4,5,8,6,7,9,10,13,11,12,19,20,21,14,15,22,18,16,17,23,24,27,
%N A057118 Permutation of natural numbers induced by the automorphism df->bf (switch from the Depth First to the Breadth First coding for the binary trees) acting on the planar binary trees encoded by A014486.
%H A057118 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%Y A057118 Restriction of the automorphism A072089 to the plane binary trees. Being self-embeddable, this allows us also to form the permutation A070041. Inverse permutation: A057117.

-------------------------------------------------------------------------


%I A072088
%S A072088 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,19,16,17,18,15,20,21,22,23,24,25,26,27,28,33,30,31,32,29,
%T A072088 34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,
%U A072088 64,65,66,67,68,69,70,75,72,73,74,71,76,77,78,79,93,80,98,102,84,89,86,87,88,95,90,91,92,81
%N A072088 Permutation of natural numbers induced by the automorphism gt-bf->df (switch from the Breadth First to the Depth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.
%C A072088 When restricted to the subset of plane binary trees, produces the automorphism A057117, with which this shares the property of "self-embeddability": each sub-permutation of the length A000108(n): 0; 1; 2,3; 4,5,6,7,8; 9,10,11,12,13,14,19,16,17,18,15,20,21,22; 23,24,25,26,27,28,33,30,31,32,29,34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,64; starts with the same cycle-structure as the previous sub-permutation. (i.e. the terms from the first to the sixth are fixed, the 7th and 11th are transposed, etc.), thus allowing us to construct the permutation A072619 (A072621).
%R A072088
%H A072088 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072088 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072088 0,3
%K A072088 nonn,new
%A A072088 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072088 Inverse permutation: A072089. Cf. also A014486, A057117, A072619.
%D A072088
%p A072088

%I A072089
%S A072089 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,19,16,17,18,15,20,21,22,23,24,25,26,27,28,33,30,31,32,29,
%T A072089 34,35,36,37,39,51,56,52,42,53,44,45,46,43,48,49,50,38,60,47,54,61,40,57,58,59,41,55,62,63,
%U A072089 64,65,66,67,68,69,70,75,72,73,74,71,76,77,78,79,81,93,98,94,84,95,86,87,88,85,90,91,92,80
%N A072089 Permutation of natural numbers induced by the automorphism gt-df->bf (switch from the Depth First to the Breadth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.
%C A072089 When restricted to the subset of plane binary trees, produces the automorphism A057118, and being "self-embeddable", this allows us also to construct the permutation A072620 (A072622). [See comment at A072088].
%R A072089
%H A072089 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072089 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072089 0,3
%K A072089 nonn,new
%A A072089 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072089 Inverse permutation: A072088. Cf. also A014486, A057118, A072620.
%D A072089
%p A072089

%I A072090
%S A072090 0,1,3,2,7,8,4,5,6,17,18,20,21,22,10,9,11,12,13,14,15,19,16,45,46,48,49,50,54,55,57,58,59,61,
%T A072090 62,63,64,26,27,23,24,25,29,28,30,31,32,33,34,35,36,38,37,39,40,41,51,52,56,60,42,43,44,47,
%U A072090 53,129,130,132,133,134,138,139,141,142,143,145,146,147,148,157,158,160,161,162,166,167,169
%N A072090 Permutation of natural numbers induced by the automorphism cdr_robr_car! acting on the parenthesizations encoded by A014486.
%R A072090
%H A072090 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072090 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072090 0,3
%K A072090 nonn,new
%A A072090 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072090 Inverse permutation: A072091, and also its car/cdr-flipped conjugate, i.e. A072090(n) = A057163(A072091(A057163(n))). Cf. also A071655-A071660, A072092-A072095
%D A072090
%o A072090 (Scheme function implementing this automorphism on list-structures:)
%o A072090 (define (cdr_robr_car! s) (cond ((not (pair? s))) ((not (pair? (car s))) (swap! s)) (else (cdr_robr_car! (cdr s)) (robr! s) (cdr_robr_car! (car s)))) s)
%o A072090 (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
%o A072090 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))


%I A072091
%S A072091 0,1,3,2,6,7,8,4,5,15,14,16,17,18,19,20,22,9,10,21,11,12,13,39,40,41,37,38,43,42,44,45,46,47,
%T A072091 48,49,50,52,51,53,54,55,60,61,62,23,24,63,25,26,27,56,57,64,28,29,58,30,31,32,59,33,34,35,
%U A072091 36,113,112,114,115,116,117,118,120,107,108,119,109,110,111,123,124,125,121,122,127,126,128
%N A072091 Permutation of natural numbers induced by the automorphism car_robl_cdr! acting on the parenthesizations encoded by A014486.
%R A072091
%H A072091 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072091 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072091 0,3
%K A072091 nonn,new
%A A072091 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072091 Inverse permutation: A072090, and also its car/cdr-flipped conjugate, i.e. A072091(n) = A057163(A072090(A057163(n))). Cf. also A071655-A071660, A072092-A072095
%D A072091
%o A072091 (Scheme function implementing this automorphism on list-structures:)
%o A072091 (define (car_robl_cdr! s) (cond ((not (pair? s))) ((not (pair? (cdr s))) (swap! s)) (else (car_robl_cdr! (car s)) (robl! s) (car_robl_cdr! (cdr s)))) s)
%o A072091 (define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))
%o A072091 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))


%I A072092
%S A072092 0,1,3,2,7,8,4,6,5,17,18,20,21,22,9,10,14,19,16,11,12,15,13,45,46,48,49,50,54,55,57,58,59,61,
%T A072092 62,63,64,23,24,25,26,27,37,38,51,56,60,42,44,53,47,28,29,30,31,32,39,40,43,52,33,34,35,41,
%U A072092 36,129,130,132,133,134,138,139,141,142,143,145,146,147,148,157,158,160,161,162,166,167,169
%N A072092 Permutation of natural numbers induced by the automorphism car_robr_car! acting on the parenthesizations encoded by A014486.
%R A072092
%H A072092 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072092 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072092 0,3
%K A072092 nonn,new
%A A072092 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072092 Inverse permutation: A072093. The car/cdr-flipped conjugate of A072095, i.e. A072092(n) = A057163(A072095(A057163(n))). Cf. also A071655-A071660, A072090-A072091
%D A072092
%o A072092 (Scheme function implementing this automorphism on list-structures:)
%o A072092 (define (car_robr_car! s) (cond ((not (pair? s))) ((not (pair? (car s))) (swap! s)) (else (car_robr_car! (car s)) (robr! s) (car_robr_car! (car s)))) s)
%o A072092 (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
%o A072092 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))



%I A072093
%S A072093 0,1,3,2,6,8,7,4,5,14,15,19,20,22,16,21,18,9,10,17,11,12,13,37,38,39,40,41,51,52,53,54,55,60,
%T A072093 61,62,64,42,43,56,57,63,47,58,48,23,24,50,25,26,27,44,59,49,28,29,45,30,31,32,46,33,34,35,
%U A072093 36,107,108,109,110,111,112,113,114,115,116,117,118,119,120,149,150,151,152,153,154,155,156
%N A072093 Permutation of natural numbers induced by the automorphism car_robl_car! acting on the parenthesizations encoded by A014486.
%R A072093
%H A072093 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072093 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072093 0,3
%K A072093 nonn,new
%A A072093 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072093 Inverse permutation: A072092. The car/cdr-flipped conjugate of A072094, i.e. A072093(n) = A057163(A072094(A057163(n))). Cf. also A071655-A071660, A072090-A072091
%D A072093
%o A072093 (Scheme function implementing this automorphism on list-structures:)
%o A072093 (define (car_robl_car! s) (cond ((not (pair? s))) ((not (pair? (cdr s))) (swap! s)) (else (car_robl_car! (car s)) (robl! s) (car_robl_car! (car s)))) s)
%o A072093 (define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))
%o A072093 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))


%I A072094
%S A072094 0,1,3,2,7,8,5,4,6,17,18,20,21,22,13,12,10,9,11,15,14,16,19,45,46,48,49,50,54,55,57,58,59,61,
%T A072094 62,63,64,35,36,32,31,34,26,27,24,23,25,29,28,30,33,41,40,38,37,39,43,42,44,47,52,51,53,56,
%U A072094 60,129,130,132,133,134,138,139,141,142,143,145,146,147,148,157,158,160,161,162,166,167,169
%N A072094 Permutation of natural numbers induced by the automorphism cdr_robr_cdr! acting on the parenthesizations encoded by A014486.
%R A072094
%H A072094 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072094 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072094 0,3
%K A072094 nonn,new
%A A072094 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072094 Inverse permutation: A072095. The car/cdr-flipped conjugate of A072093, i.e. A072094(n) = A057163(A072093(A057163(n))). Cf. also A071655-A071660, A072090-A072091
%D A072094
%o A072094 (Scheme function implementing this automorphism on list-structures:)
%o A072094 (define (cdr_robr_cdr! s) (cond ((not (pair? s))) ((not (pair? (car s))) (swap! s)) (else (cdr_robr_cdr! (cdr s)) (robr! s) (cdr_robr_cdr! (cdr s)))) s)
%o A072094 (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
%o A072094 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))



%I A072095
%S A072095 0,1,3,2,7,6,8,4,5,17,16,18,15,14,20,19,21,9,10,22,11,12,13,45,44,46,42,43,48,47,49,40,39,50,
%T A072095 41,37,38,54,53,55,52,51,57,56,58,23,24,59,25,26,27,61,60,62,28,29,63,30,31,32,64,33,34,35,
%U A072095 36,129,128,130,127,126,132,131,133,121,125,134,122,124,123,138,137,139,135,136,141,140,142
%N A072095 Permutation of natural numbers induced by the automorphism cdr_robl_cdr! acting on the parenthesizations encoded by A014486.
%R A072095
%H A072095 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072095 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072095 0,3
%K A072095 nonn,new
%A A072095 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072095 Inverse permutation: A072094. The car/cdr-flipped conjugate of A072092, i.e. A072095(n) = A057163(A072092(A057163(n))). Cf. also A071655-A071660, A072090-A072091
%D A072095
%o A072095 (Scheme function implementing this automorphism on list-structures:)
%o A072095 (define (cdr_robl_cdr! s) (cond ((not (pair? s))) ((not (pair? (cdr s))) (swap! s)) (else (cdr_robl_cdr! (cdr s)) (robl! s) (cdr_robl_cdr! (cdr s)))) s)
%o A072095 (define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))
%o A072095 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))



%I A072619
%S A072619 0,1,2,3,4,5,10,7,8,9,6,11,12,13,14,28,15,33,37,19,24,21,22,23,30,25,26,27,16,18,20,31,38,17,
%T A072619 34,35,36,29,32,39,40,41,42,84,43,98,112,44,46,45,103,107,85,117,121,126,56,70,89,75,79,61,
%U A072619 66,63,64,65,72,67,68,69,57,114,91,73,80,100,76,77,78,94,74,81,82,83,47,52,86,54,55,58,60,62
%N A072619 Permutation of natural numbers obtained from the permutation A072088 (zero-based).
%C A072619 See the comment at A072088.
%R A072619
%H A072619 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072619 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072619 0,3
%K A072619 nonn,new
%A A072619 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072619 A072619(n) = A072621(n+1)-1. Inverse permutation: A072620. Cf. also A072088, A038776.
%D A072619
%p A072619


%I A072620
%S A072620 0,1,2,3,4,5,10,7,8,9,6,11,12,13,14,16,28,33,29,19,30,21,22,23,20,25,26,27,15,37,24,31,38,17,
%T A072620 34,35,36,18,32,39,40,41,42,44,47,49,48,84,112,98,103,99,85,107,87,88,56,70,89,100,90,61,91,
%U A072620 63,64,65,62,67,68,69,57,94,66,73,80,59,76,77,78,60,74,81,82,83,43,52,86,117,126,58,114,72
%N A072620 Permutation of natural numbers obtained from the permutation A072089 (zero-based).
%C A072620 See the comment at A072088.
%R A072620
%H A072620 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072620 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072620 0,3
%K A072620 nonn,new
%A A072620 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%Y A072620 A072620(n) = A072622(n+1)-1. Inverse permutation: A072619. Cf. also A072089, A070041.
%D A072620
%p A072620


%I A072621
%S A072621 1,2,3,4,5,6,11,8,9,10,7,12,13,14,15,29,16,34,38,20,25,22,23,24,31,26,27,28,17,19,21,32,39,
%T A072621 18,35,36,37,30,33,40,41,42,43,85,44,99,113,45,47,46,104,108,86,118,122,127,57,71,90,76,80,
%U A072621 62,67,64,65,66,73,68,69,70,58,115,92,74,81,101,77,78,79,95,75,82,83,84,48,53,87,55,56,59,61
%N A072621 Permutation of natural numbers obtained from the permutation A072088 (one-based).
%C A072621 See the comment at A072088.
%R A072621
%H A072621 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072621 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072621 1,2
%K A072621 nonn,new
%A A072621 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%D A072621
%Y A072621 A072621(n) = A072619(n-1)+1. Inverse permutation: A072622. Cf. also A038776.
%p A072621


%I A072622
%S A072622 1,2,3,4,5,6,11,8,9,10,7,12,13,14,15,17,29,34,30,20,31,22,23,24,21,26,27,28,16,38,25,32,39,
%T A072622 18,35,36,37,19,33,40,41,42,43,45,48,50,49,85,113,99,104,100,86,108,88,89,57,71,90,101,91,62,
%U A072622 92,64,65,66,63,68,69,70,58,95,67,74,81,60,77,78,79,61,75,82,83,84,44,53,87,118,127,59,115
%N A072622 Permutation of natural numbers obtained from the permutation A072089 (one-based).
%C A072622 See the comment at A072088.
%R A072622
%H A072622 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(Includes the complete Scheme program for computing this sequence)</I>
%H A072622 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%O A072622 1,2
%K A072622 nonn,new
%A A072622 Antti Karttunen (my_firstname.my_surname@iki.fi) Jun 25 2002
%D A072622
%Y A072622 A072622(n) = A072620(n-1)+1. Inverse permutation: A072621. Cf. also A070041.
%p A072622




---------------------------------------------------------------------


Yours,

Antti Karttunen