%I #12 Jan 12 2024 07:47:51

%S 0,0,0,0,1,0,0,1,1,0,0,1,2,1,0,0,1,1,1,1,0,0,1,2,3,2,1,0,0,1,2,1,1,2,

%T 1,0,0,1,2,1,4,1,2,1,0,0,1,1,3,2,2,3,1,1,0,0,1,1,3,2,5,2,3,1,1,0,0,1,

%U 2,3,1,2,2,1,3,2,1,0,0,1,2,1,1,1,6,1,1,1,2,1,0,0,1,2,1,4,1,3,3,1,4,1,2,1,0,0,1,2,1,4,2,3,7,3,2,4,1,2,1,0

%N Array A(x,y): the greatest common subtree (intersect) 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 Note that together with A082860 this forms a distributive lattice, thus it is possible to compute this function also with the binary AND-operation (A004198) with the help of appropriate mapping functions. I.e. we have A(x,y) = A082857(A004198(A082856(x), A082856(y))).

%H Antti Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/ACO1.htm">Alternative Catalan Orderings</a> (with the complete Scheme source)

%H <a href="/index/La#Lattices">Index entries for sequences related to lattices</a>

%o (Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)

%o (define (A082858 n) (A080300 (parenthesization->binexp (GCSB (binexp->parenthesization (A014486 (A025581 n))) (binexp->parenthesization (A014486 (A002262 n)))))))

%o (define (GCSB t1 t2) (cond ((or (not (pair? t1)) (not (pair? t2))) (list)) (else (cons (GCSB (car t1) (car t2)) (GCSB (cdr t1) (cdr t2))))))

%o (define (A082858v2 n) (A082857 (A004198bi (A082856 (A025581 n)) (A082856 (A002262 n)))))

%Y Cf. A072764. The lower/upper triangular region: A082859. Cf. A080300, A025581, A002262.

%K nonn,tabl

%O 0,13

%A _Antti Karttunen_, May 06 2003