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Search: id:A082858
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| A082858 |
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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). |
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4
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| 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, 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, 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
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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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))).
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LINKS
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A. Karttunen, Alternative Catalan Orderings (with the complete Scheme source)
Index entries for sequences related to lattices
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PROGRAM
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(Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)
(define (A082858 n) (A080300 (parenthesization->binexp (GCSB (binexp->parenthesization (A014486 (A025581 n))) (binexp->parenthesization (A014486 (A002262 n)))))))
(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))))))
(define (A082858v2 n) (A082857 (A004198bi (A082856 (A025581 n)) (A082856 (A002262 n)))))
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CROSSREFS
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Cf. A072764. The lower/upper triangular region: A082859. Cf. A080300, A025581, A002262.
Sequence in context: A118229 A117201 A060953 this_sequence A115953 A136567 A109708
Adjacent sequences: A082855 A082856 A082857 this_sequence A082859 A082860 A082861
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen (MyFirstname.MySurname(AT)iki.fi) May 06 2003
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