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Search: id:A082856
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| A082856 |
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Recursive binary interleaving code for rooted plane binary trees, as ordered by A014486. |
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+0
4
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| 0, 1, 3, 5, 11, 35, 7, 21, 69, 139, 2059, 43, 547, 8227, 15, 39, 23, 277, 4117, 71, 85, 1093, 16453, 32907, 8388747, 2187, 526347, 134219787, 171, 2091, 555, 131619, 33554979, 8235, 8739, 2105379, 536879139, 143, 2063, 47, 551, 8231, 31, 55, 279, 65813, 16777493, 4119, 4373, 1052693, 268439573, 79, 103, 87, 341, 4181, 1095, 1109
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This encoding has a property that the greatest common subtree i.e. the intersect (or the least common supertree, the union) of any two trees can be obtained by simply computing the binary-AND (A004198) (or respectively: binary-OR, A003986) of the corresponding codes. See A082858-A082860.
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LINKS
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A. Karttunen, Alternative Catalan Orderings (with the complete Scheme source)
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EXAMPLE
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The empty tree . has code 0, the tree of two edges (and leaves) \/ has code 1 and in general tree's code is obtained by interleaving into odd and even bits (above bit-0, which is always 1 for non-empty trees) the codes for the left and right hand side subtrees of the tree.
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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 A082856 (compose-funs bin-interleave binexp->parenthesization A014486))
(define (bin-interleave bt) (cond ((not (pair? bt)) 0) (else (1+ (* 2 (+ (* 2 (A000695 (bin-interleave (car bt)))) (A000695 (bin-interleave (cdr bt)))))))))
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CROSSREFS
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Inverse: A082857. Cf. A072634-A072637, A075173-A075174, A000695.
Sequence in context: A154939 A121926 A063499 this_sequence A060881 A035345 A162250
Adjacent sequences: A082853 A082854 A082855 this_sequence A082857 A082858 A082859
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (MyFirstname.MySurname(AT)iki.fi) May 06 2003
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