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A127300 Signature-permutation of A057164-conjugate of the inverse of Elizalde's and Deutsch's 2003 bijection for Dyck paths. 5
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 (list; graph; refs; listen; history; text; internal format)
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 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

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)