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A072634 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A054238 as the pairing function N X N -> N.

%I A072634 #9 Dec 20 2017 14:42:56
%S A072634 0,1,3,2,11,9,4,6,5,139,131,33,41,35,12,10,8,70,66,7,17,21,18,32907,
%T A072634 32779,2051,2179,2059,161,137,129,8233,8201,43,515,547,521,140,132,34,
%U A072634 42,36,16,14,72,16454,16390,68,1026,1090,1030,15,13,19,81,69,23,65
%N A072634 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A054238 as the pairing function N X N -> N.
%H A072634 Antti Karttunen, <a href="https://oeis.org/wiki/User:Antti_Karttunen/Catalania/Alternative_Catalan_Orderings">Alternative Catalan Orderings</a>
%H A072634 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A072634 (Scheme)
%o A072634 ;; Functions below show the essential idea:
%o A072634 (define A072634 (lexrank->arithrank-bijection packA054238))
%o A072634 (define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
%o A072634 (define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
%o A072634 (define (packA054238 x y) (+ (A000695 x) (* 2 (A000695 y))))
%Y A072634 Inverse permutation: A072635.
%Y A072634 Cf. A014486, A000695, A054238, A071651, A072636, A072646, A072656, A072658, A072644.
%Y A072634 Cf. also A296689.
%K A072634 nonn
%O A072634 0,3
%A A072634 _Antti Karttunen_, Jun 02 2002