A127300 Signature-permutation of A057164-conjugate of the inverse of Elizalde's and Deutsch's 2003 bijection for Dyck paths.

0, 1, 3, 2, 8, 4, 7, 6, 5, 22, 11, 17, 16, 12, 21, 9, 20, 19, 10, 18, 14, 13, 15, 64, 33, 48, 47, 34, 58, 23, 57, 56, 24, 49, 37, 35, 38, 63, 30, 45, 44, 31, 62, 28, 61, 60, 29, 46, 42, 32, 43, 59, 25, 54, 53, 26, 50, 39, 36, 40, 55, 51, 27, 52, 41, 196, 102, 145, 144, 103

Offset

0,3

Comments

Used to construct the inverse for A127291.

References

Emeric Deutsch and Sergi Elizalde, A simple and unusual bijection for Dyck paths and its consequences, Annals of Combinatorics, 7 (2003), no. 3, 281-297.

Links

Table of n, a(n) for n=0..69.

Index entries for signature-permutations of Catalan automorphisms

Prog

(MIT/GNU Scheme)
(define (A127300 n) (A080300 (transpos-list->A014486 (A127300-aux1 (A014486 n)))))
(define (transpos-list->A014486 tplist) (fold-left (lambda (s p) (+ s (expt 2 (max (car p) (cdr p))))) 0 tplist))
(define (a127300-aux1 n) (if (zero? n) (list) (let loop ((n n) (tplist1 (list)) (tplist2 (list)) (i 0) (j (A000523 n)) (b 1)) (cond ((zero? n) (append tplist1 tplist2)) ((even? n) (loop (/ n 2) tplist2 (cons (cons '() i) tplist1) j (+ i b) (- b))) ((assq '() tplist1) => (lambda (p) (set-car! p i) (loop (/ (- n 1) 2) tplist2 tplist1 j (+ i b) (- b)))) ((rassq '() tplist2) => (lambda (p) (set-car! p i) (loop (/ (- n 1) 2) tplist2 tplist1 j (+ i b) (- b)))) (else (error "n not in A014486!")))))) ;; Returns a list of non-crossing transpositions.
(define (rassq key al) (let loop ((al al) (last-found #f)) (cond ((null? al) last-found) ((eq? (caar al) key) (loop (cdr al) (car al))) (else (loop (cdr al) last-found))))) ;; (rassq key al) is essentially the same as: (assq key (reverse al))

Crossrefs

Inverse: A127299. a(n) = A057164(A127292(A057164(n))) = A127290(A057164(n)). Cf. A014486.

Sequence in context: A143515 A082333 A162728 * A129199 A211164 A097018

Adjacent sequences: A127297 A127298 A127299 * A127301 A127302 A127303

Keyword

nonn

Author

Antti Karttunen, Jan 16 2007

Status

approved