id:A086431 - OEIS Search Results

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Involution of natural numbers induced by the gatomorphism gma086431 acting on symbolless S-expressions encoded by A014486/A063171.

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0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 10, 12, 13, 17, 18, 16, 14, 15, 21, 20, 19, 22, 23, 28, 25, 30, 33, 24, 29, 26, 31, 32, 27, 35, 34, 36, 45, 48, 46, 49, 50, 44, 47, 42, 37, 39, 43, 38, 40, 41, 58, 59, 57, 54, 55, 56, 53, 51, 52, 63, 62, 61, 60, 64, 65, 79, 70, 84, 93 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`This gatomorphism reflects the interpretations (pp)-(rr) of Stanley, obtained with the "descending slope mapping" from the Dyck paths encoded by A014486.`
	LINKS	`A. Karttunen, Noncrossing Murasaki diagrams obtained via descending slope mapping illustrated up to seven sticks` `A. Karttunen, Gatomorphisms (With the complete Scheme source)` `R. P. Stanley, Exercises on Catalan and Related Numbers (including 66 combinatorial interpretations)` `Index entries for signature-permutations induced by Catalan automorphisms`
	EXAMPLE	`Map the Dyck paths (Stanley's interpretation (i)) to noncrossing Murasaki-diagrams (Stanley's interpretation (rr)) by drawing a vertical line above each descending slope \, and connect those vertical lines that originate from the same height without any lower valleys between, as in illustration below:` `..................................................` `.....___________..................................` `....\|...\|....._.\|.................................` `....\|..\|\|...\|\|.\|\|..................___________....` `....\|..\|\|...\|\|.\|\|.................\|...\|...._..\|...` `....\|..\|\|../\\|.\|\|..i.e..equal.to..\|.\|.\|.\|.\|.\|.\|...` `....\|./\\|./..\/\\|.................\|.\|.\|.\|.\|.\|.\|...` `.../\/..\/......\.................\|.\|.\|.\|.\|.\|.\|...` `...10110011100100=11492=A014486(250)` `Now the gatomorphism gma086431 gives the parenthesization such that the corresponding Murasaki-diagram is a reflection of the original one:` `.....___________..................................` `....\|...._..\|...\|.................................` `....\|...\|.\|\|\|..\|\|..................___________....` `....\|...\|.\|\|\|..\|\|.................\|.._....\|...\|...` `....\|../\/\\|\|..\|\|..i.e..equal.to..\|.\|.\|.\|.\|.\|.\|...` `....\|./....\\|./\\|.................\|.\|.\|.\|.\|.\|.\|...` `.../\/......\/..\.................\|.\|.\|.\|.\|.\|.\|...` `...10111010001100=11916=A014486(296)` `So we have A086431(250)=296 and A086431(296)=250.`
	CROSSREFS	`a(n) = A057164(A085161(A057164(n))) = A086425(A057164(A086426(n))). Occurs in A073200. Cf. also A086427, A086430.` `Number of cycles: A007123. Number of fixed points: A001405. (In range [A014137(n-1)..A014138(n-1)] of this permutation.).` `Sequence in context: A130935 A082325 A069787 this_sequence A143579 A100806 A102451` `Adjacent sequences: A086428 A086429 A086430 this_sequence A086432 A086433 A086434`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (Firstname.Surname(AT)iki.fi), Jun 23 2003`

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Last modified November 21 14:49 EST 2008. Contains 150807 sequences.

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