cp's OEIS Frontend

A082860 Array A(x,y): the least common supertree (union) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).

%I A082860 #12 Jan 12 2024 07:48:03
%S A082860 0,1,1,2,1,2,3,2,2,3,4,3,2,3,4,5,4,6,6,4,5,6,5,4,3,4,5,6,7,6,5,14,14,
%T A082860 5,6,7,8,7,6,15,4,15,6,7,8,9,8,16,6,11,11,6,16,8,9,10,9,19,7,14,5,14,
%U A082860 7,19,9,10,11,10,9,8,42,15,15,42,8,9,10,11,12,11,10,37,51,43,6,43,51,37,10,11,12,13,12,11,38,9,52,16,16,52,9,38,11,12,13,14,13,12
%N A082860 Array A(x,y): the least common supertree (union) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).
%C A082860 Note that together with A082858 this forms a distributive lattice, thus it is possible to compute this function also with the binary OR-operation (A003986) with the help of appropriate mapping functions. I.e. we have A(x,y) = A082857(A003986(A082856(x), A082856(y))).
%H A082860 Antti Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/ACO1.htm">Alternative Catalan Orderings</a> (with the complete Scheme source)
%H A082860 <a href="/index/La#Lattices">Index entries for sequences related to lattices</a>
%o A082860 (Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)
%o A082860 (define (A082860 n) (A080300 (parenthesization->binexp (LCSB (binexp->parenthesization (A014486 (A025581 n))) (binexp->parenthesization (A014486 (A002262 n)))))))
%o A082860 (define (LCSB t1 t2) (cond ((and (not (pair? t1)) (not (pair? t2))) (list)) (else (cons (LCSB (car* t1) (car* t2)) (LCSB (cdr* t1) (cdr* t2))))))
%o A082860 (define (car* p) (if (pair? p) (car p) p))
%o A082860 (define (cdr* p) (if (pair? p) (cdr p) p))
%o A082860 (define (A082860v2 n) (A082857 (A003986bi (A082856 (A025581 n)) (A082856 (A002262 n)))))
%Y A082860 The lower/upper triangular region: A082861. Cf. A072764, A080300, A025581, A002262.
%K A082860 nonn,tabl
%O A082860 0,4
%A A082860 _Antti Karttunen_, May 06 2003