|
%I #9 Jan 30 2024 04:37:35
%S 0,0,1,0,0,0,0,0,0,0,0,0,2,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,5,0
%N Inverse function of N -> N injection A057123.
%C a(0)=0 because A057123(0)=0, but a(n) = 0 also for those n which do not occur as values of A057123. All positive natural numbers occur here once.
%C If g(n) = A083927(f(A057123(n))) then we can say that Catalan bijection g embeds into Catalan bijection f in scale n:2n, using the obvious binary tree -> general tree embedding. E.g. we have: A057163 = A083927(A057164(A057123(n))), A057117 = A083927(A072088(A057123(n))), A057118 = A083927(A072089(A057123(n))), A069770 = A083927(A072796(A057123(n))), A072797 = A083927(A072797(A057123(n))).
%H Antti Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a>
%o (Scheme-function showing the essential idea. For the full source, follow the "Catalan bijections" link.)
%o (define (Tree2BinTree_if_possible gt) (call-with-current-continuation (lambda (e) (let recurse ((gt gt)) (cond ((not (pair? gt)) gt) ((eq? 2 (length gt)) (cons (recurse (car gt)) (recurse (cadr gt)))) (else (e '())))))))
%Y a(A057123(n)) = n for all n. Cf. A083925-A083926, A083928-A083929, A083935.
%K nonn
%O 0,13
%A _Antti Karttunen_, May 13 2003
|
