0,3

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.

A. Karttunen, Gatomorphisms

Index entries for sequences that are permutations of the natural numbers

(Scheme functions below show the essential idea. For a complete source, follow the "Gatomorphisms" link.)

(define A072787 (lexrank->arithrank-bijection packA072734))

(define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))

(define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))

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

Sequence in context: A113782 A090868 A125675 this_sequence A107271 A104633 A102022

Adjacent sequences: A072784 A072785 A072786 this_sequence A072788 A072789 A072790

nonn

Antti Karttunen Jun 12 2002