A072787 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A072734 as the packing bijection N X N -> N.

0, 1, 3, 2, 6, 5, 13, 8, 4, 14, 10, 36, 20, 9, 25, 19, 24, 11, 12, 18, 38, 16, 7, 44, 27, 209, 77, 21, 105, 66, 104, 28, 35, 65, 230, 54, 15, 34, 33, 75, 43, 26, 85, 50, 40, 37, 22, 31, 191, 67, 23, 51, 41, 69, 107, 68, 49, 92, 30, 29, 32, 56, 211, 46, 17, 299, 120, 5671

Offset: 0

Author

Antti Karttunen, Jun 12 2002

Keywords

• nonn

Comments

This ranking scheme condenses the structures of the same size (cf. A072789) somewhat better than scheme presented in A072656 (which uses the N X N -> N bijection A072793). Compare the sequences A072790 and A072640 giving the max positions where the last structure with size n will occur in these orderings and the respective binary widths A072791 & A072642. However, by using the second or third power of the bijection A072734 one gets even better results in a certain range.

Links

• A. Karttunen, Gatomorphisms
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A072788. Cf. also A014486, A072734, A072789.