cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A082858 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).

Original entry on oeis.org

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
Offset: 0

Views

Author

Antti Karttunen, May 06 2003

Keywords

Comments

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))).

Links

Crossrefs

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

A082856 Recursive binary interleaving code for rooted plane binary trees, as ordered by A014486.

Original entry on oeis.org

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
Offset: 0

Views

Author

Antti Karttunen, May 06 2003

Keywords

Comments

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.

Examples

			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 nonempty trees) the codes for the left and right hand side subtrees of the tree.

Links

Crossrefs

Inverse: A082857. Cf. A072634-A072637, A075173-A075174, A000695.

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).

Original entry on oeis.org

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, 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, 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
Offset: 0

Views

Author

Antti Karttunen, May 06 2003

Keywords

Comments

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))).

Links

Crossrefs

The lower/upper triangular region: A082861. Cf. A072764, A080300, A025581, A002262.
Showing 1-3 of 3 results.

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